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Expectation Propogation for approximate inference in dynamic Bayesian networksDec 12 2012We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges IN many practical cases, but NOT always.We derive ... More

Dynamic Mechanism Design for Markets with Strategic ResourcesFeb 14 2012The assignment of tasks to multiple resources becomes an interesting game theoretic problem, when both the task owner and the resources are strategic. In the classical, nonstrategic setting, where the states of the tasks and resources are observable by ... More

Dynamic Mechanism Design with Interdependent ValuationsJun 25 2015We consider an infinite horizon dynamic mechanism design problem with interdependent valuations. In this setting the type of each agent is assumed to be evolving according to a first order Markov process and is independent of the types of other agents. ... More

Dashboard Mechanisms for Online MarketplacesMay 14 2019This paper gives a theoretical model for design and analysis of mechanisms for online marketplaces where a bidding dashboard enables the bid-optimization of long-lived agents. We assume that a good allocation algorithm exists when given the true values ... More

An Incentive Compatible Multi-Armed-Bandit Crowdsourcing Mechanism with Quality AssuranceJun 27 2014Jun 17 2015Consider a requester who wishes to crowdsource a series of identical binary labeling tasks to a pool of workers so as to achieve an assured accuracy for each task, in a cost optimal way. The workers are heterogeneous with unknown but fixed qualities and ... More

Gaussian Integers, Rings, Finite Fields, and the Magic Square of SquaresAug 08 2019Aug 12 2019We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular case in which said extension is assumed to be the Gaussian ... More

Gaussian Integers, Rings, Finite Fields, and the Magic Square of SquaresAug 08 2019We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular case in which said extension is assumed to be the Gaussian ... More

A bivariate risk model with mutual deficit coverageJan 13 2015May 04 2015We consider a bivariate Cramer-Lundberg-type risk reserve process with the special feature that each insurance company agrees to cover the deficit of the other. It is assumed that the capital transfers between the companies are instantaneous and incur ... More

Bioperational Multisets in Various Semi-ringsAug 08 2019One can find lists of whole numbers having equal sum and product. We call such a creature a bioperational multiset. No one seems to have seriously studied them in areas outside whole numbers such as the rationals, Gaussian integers, or semi-rings. We ... More

Useful martingales for stochastic storage processes with Lévy-type input and decomposition resultsDec 20 2011Oct 08 2012This paper has been withdrawn by the author as it has been divided into two separate papers.

Decomposition results for stochastic storage processes and queues with alternating Lévy inputsOct 08 2012In this paper we generalize known workload decomposition results for L\'{e}vy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases are polling systems with either compound Poisson or more general L\'{e}vy ... More

Useful martingales for stochastic storage processes with Lévy-type inputOct 08 2012In this paper we generalize the martingale of Kella and Whitt to the setting of L\'{e}vy-type processes and show that the (local) martingales obtained are in fact square integrable martingales which upon dividing by the time index converge to zero a.s. ... More

Two coupled Levy queues with independent inputJun 10 2013We consider a pair of coupled queues driven by independent spectrally-positive Levy processes. With respect to the bi-variate workload process this framework includes both the coupled processor model and the two-server fluid network with independent Levy ... More

Variational inference for neural network matrix factorization and its application to stochastic blockmodelingMay 11 2019We consider the probabilistic analogue to neural network matrix factorization (Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and fit with variational inference. We find that a linear model fit with variational inference can ... More

On queues with service and interarrival times depending on waiting timesApr 22 2014We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, B-A+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley equation for the ... More

Domination properties and extension of positive compact operators on pre-Riesz spacesSep 16 2018This paper concerns positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space to the Riesz completion. It extends the order continuous norms in pre-Riesz spaces to Riesz completions. The compactness ... More

Stochastic Integration in Banach Spaces using a product structure with partial orderOct 28 2009Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.

On open problems in polling systemsAug 01 2014In the present paper we address two open problems concerning polling systems, viz., queueing systems consisting of multiple queues attended by a single server that visits the queues one at a time. The first open problem deals with a system consisting ... More

A Two-Queue Polling Model with Two Priority Levels in the First QueueAug 01 2014In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and low priority ... More

Towards Universal End-to-End Affect Recognition from Multilingual Speech by ConvNetsJan 19 2019We propose an end-to-end affect recognition approach using a Convolutional Neural Network (CNN) that handles multiple languages, with applications to emotion and personality recognition from speech. We lay the foundation of a universal model that is trained ... More

Second derivatives of norms and contractive complementation in vector-valued spacesNov 02 2005We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces $\ell_p(X)$, where $X$ is a Banach space with a 1-unconditional basis and $p \in (1,2)\cup (2,\infty)$. If the norm of $X$ is twice continuously differentiable ... More

Disjointness preserving $\mathrm{C}_0$-semigroups and local operators on ordered Banach spacesNov 04 2016We generalize results concerning $\mathrm{C}_0$-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving $\mathrm{C}_0$-semigroup is local. Some basic properties of local operators are ... More

Analysis and optimization of vacation and polling models with retrialsJan 22 2015Feb 02 2016We study a vacation-type queueing model, and a single-server multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) ... More

DNStamp: Short-lived Trusted TimestampingJul 22 2013Mar 11 2014Trusted timestamping consists in proving that certain data existed at a particular point in time. Existing timestamping methods require either a centralized and dedicated trusted service or the collaboration of other participants using the timestamping ... More

Networks of $\cdot/G/\infty$ Server Queues with Shot-Noise-Driven Arrival IntensitiesAug 17 2016Sep 30 2016We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends to display ... More

Helium-Star Mass Loss and its Implications for Black-Hole Formation and Supernova ProgenitorsMar 19 2002Recently the observationally derived stellar-wind mass-loss rates for Wolf-Rayet stars, or massive naked helium stars, have been revised downwards by a substantial amount. We present evolutionary calculations of helium stars incorporating such revised ... More

An empirical study of passive 802.11 Device FingerprintingApr 25 2014802.11 device fingerprinting is the action of characterizing a target device through its wireless traffic. This results in a signature that may be used for identification, network monitoring or intrusion detection. The fingerprinting method can be active ... More

Queue lengths and workloads in polling systemsJun 06 2011Oct 17 2011We consider a polling system: a queueing system of $N\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating function $\mathscr ... More

Bands in partially ordered vector spaces with order unitMay 15 2014In an Archimedean directed partially ordered vector space $X$ one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover $Y$ of $X$. If $X$ has an order unit, $Y$ can be represented as $C(\Omega)$, ... More

A Polling Model with Multiple Priority LevelsAug 01 2014In this paper we consider a single-server cyclic polling system. Between visits to successive queues, the server is delayed by a random switch-over time. The order in which customers are served in each queue is determined by a priority level that is assigned ... More

Networks of $\cdot/G/\infty$ Server Queues with Shot-Noise-Driven Arrival IntensitiesAug 17 2016Mar 13 2017We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends to display ... More

Convergence of the all-time supremum of a Lévy process in the heavy-traffic regimeJul 01 2010Feb 09 2011In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and ... More

Disjointness preserving $\mathrm{C}_0$-semigroups and local operators on ordered Banach spacesNov 04 2016Jul 30 2017We generalize results concerning $\mathrm{C}_0$-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving $\mathrm{C}_0$-semigroup is local. Some basic properties of local operators are ... More

HR4049: signature of nova nucleosynthesis ?Aug 16 2004The post-Asymptotic Giant Branch (AGB) star HR4049 is in an eccentric binary system with a relatively short period probably surrounded by a dusty circumbinary disk. Extremely anomalous oxygen isotopic ratios, O16/O17 ~ O16/O18 ~ 7, have been measured ... More

A Polling Model with Smart CustomersAug 01 2014In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this model we study ... More

Evolution of binary stars and the effect of tides on binary populationsJan 14 2002We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova ... More

Attention-Based LSTM for Psychological Stress Detection from Spoken Language Using Distant SupervisionMay 31 2018We propose a Long Short-Term Memory (LSTM) with attention mechanism to classify psychological stress from self-conducted interview transcriptions. We apply distant supervision by automatically labeling tweets based on their hashtag content, which complements ... More

Structure and evolution of high-mass stellar mergersJul 09 2013In young dense clusters repeated collisions between massive stars may lead to the formation of a very massive star (above 100 Msun). In the past the study of the long-term evolution of merger remnants has mostly focussed on collisions between low-mass ... More

Modelling depletion by re-accretion of gas from a dusty disc in post-AGB starsAug 05 2019Aug 08 2019Many disc-type post-asymptotic giant branch (post-AGB) stars are chemically peculiar, showing underabundances of refractory elements in their photospheres that correlate with condensation temperature. The aim of this paper is to investigate how accretion ... More

Queue-length balance equations in multiclass multiserver queues and their generalizationsMay 01 2017A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. ... More

Invariant measures for stochastic functional differential equations with superlinear drift termMar 11 2009We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove tightness and ... More

Semi-analytic modelling of the europium production by neutron star mergers in the halo of the Milky WayDec 07 2018Neutron star mergers (NSM) are likely to be the main production sites for the rapid (r-) neutron capture process elements. We study the r-process enrichment of the stellar halo of the Milky Way through NSM, by tracing the typical r-process element Eu ... More

Population Synthesis of Binary Carbon-enhanced Metal-poor StarsOct 12 2009The carbon-enhanced metal-poor (CEMP) stars constitute approximately one fifth of the metal-poor ([Fe/H] ~< -2) population but their origin is not well understood. The most widely accepted formation scenario, invokes mass-transfer of carbon-rich material ... More

The Spatial Distribution of Coalescing Neutron Star Binaries: Implications for Gamma-Ray BurstsMay 16 1998Jan 15 1999We find the distribution of coalescence times, birthrates, spatial velocities, and subsequent radial offsets of coalescing neutron stars (NSs) in various galactic potentials accounting for large asymmetric kicks introduced during a supernovae. The birthrates ... More

Investigating Audio, Visual, and Text Fusion Methods for End-to-End Automatic Personality PredictionMay 02 2018May 16 2018We propose a tri-modal architecture to predict Big Five personality trait scores from video clips with different channels for audio, text, and video data. For each channel, stacked Convolutional Neural Networks are employed. The channels are fused both ... More

On the linearity of order-isomorphismsApr 12 2019A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of its engaged ... More

Pretty Private Group ManagementNov 22 2011Group management is a fundamental building block of today's Internet applications. Mailing lists, chat systems, collaborative document edition but also online social networks such as Facebook and Twitter use group management systems. In many cases, group ... More

Waiting time asymptotics in the single server queue with service in random orderJul 18 2012We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly ... More

Binary Populations of Carbon-Enhanced Metal-Poor StarsSep 26 2009We construct binary-star population nucleosynthesis models of carbon-enhanced metal poor (CEMP) stars. We compare the CEMP to EMP (extremely metal poor) ratio of our models to the observed ratio and find it is an order of magnitude too small. Through ... More

Revenue maximization in an optical router node - allocation of service windowsFeb 02 2016In this paper we study a revenue maximization problem for optical routing nodes. We model the routing node as a single server polling model with the aim to assign visit periods (service windows) to the different stations (ports) such that the mean profit ... More

Infinite-server queues with Hawkes inputJul 07 2017May 01 2018In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a Markovian nature. ... More

Lévy-driven polling systems and continuous-state branching processesJun 02 2010May 21 2015In this paper we consider a ring of $N\ge 1$ queues served by a single server in a cyclic order. After having served a queue (according to a service discipline that may vary from queue to queue), there is a switch-over period and then the server serves ... More

A queueing/inventory and an insurance risk modelOct 26 2015We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted as negative ... More

A Tandem Fluid Network with Lévy Input in Heavy TrafficDec 21 2015In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of L\'evy input, covering compound Poisson, $\alpha$-stable L\'evy motion (with $1<\alpha<2$), and Brownian motion. In our ... More

Closure Relations for Shallow Granular Flows from Particle SimulationsAug 25 2011The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed ... More

Understanding the orbital periods of CEMP-s starsSep 26 2018The chemical enrichments detected in CEMP-$s$ stars are believed to be the consequence of a mass-transfer episode from a now extinct AGB primary star. This hypothesis is borne out by the fact that most CEMP-$s$ stars exhibit RV variations suggesting that ... More

Modelling depletion by re-accretion of gas from a dusty disc in post-AGB starsAug 05 2019Many disc-type post-asymptotic giant branch (post-AGB) stars are chemically peculiar, showing underabundances of refractory elements in their photospheres that correlate with condensation temperature. The aim of this paper is to investigate how accretion ... More

Simulations of the tidal interaction and mass transfer of a star in an eccentric orbit around an intermediate-mass black hole: the case of HLX-1Oct 07 2015The X-ray source HLX-1 near the spiral galaxy ESO 243-49 is currently the best intermediate-mass black hole candidate. It has a peak bolometric luminosity of $10^{42}$ erg s$^{-1}$, which implies a mass inflow rate of $\sim10^{-4}$ MSun yr$^{-1}$, but ... More

From discrete particles to continuum fields near a boundaryAug 25 2011An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation ... More

Two queues with random time-limited pollingJan 24 2017Jul 12 2017In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service times. The ... More

A two-station queue with dependent preparation and service timesApr 22 2014We discuss a single-server multi-station alternating queue where the preparation times and the service times are auto- and cross-correlated. We examine two cases. In the first case, preparation and service times depend on a common discrete time Markov ... More

A single server queue with batch arrivals and semi-Markov servicesJan 18 2018We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and serves as ... More

Population synthesis of triple systems in the context of mergers of carbon-oxygen white dwarfsJan 08 2013Hierarchical triple systems are common among field stars yet their long-term evolution is poorly understood theoretically. In such systems Kozai cycles can be induced in the inner binary system during which the inner orbit eccentricity and the inclination ... More

Factorization identities for reflected processes, with applicationsFeb 11 2013We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be ... More

DNA twist stability changes with magnesium(2+) concentrationDec 30 2014For an understanding of DNA elasticity at high mechanical loads (F > 30 pN), its helical nature needs to be taken into account, in the form of coupling between the twist and stretch degrees of freedom. The prevailing model for DNA elasticity, the worm-like ... More

A Data Propagation Model for Wireless GossipingJul 23 2014Nov 04 2014Wireless sensor networks require communication protocols for efficiently propagating data in a distributed fashion. The Trickle algorithm is a popular protocol serving as the basis for many of the current standard communication protocols. In this paper ... More

Queues with random back-offsFeb 13 2013We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may ... More

AGB nucleosynthesis at low metallicity: what can we learn from carbon- and s-elements-enhanced metal-poor starsOct 25 2013CEMP-s stars are very metal-poor stars with enhanced abundances of carbon and s-process elements. They form a significant proportion of the very metal-poor stars in the Galactic halo and are mostly observed in binary systems. This suggests that the observed ... More

Resolving coiled shapes reveals new reorientation behaviors in C. elegansMar 13 2016We exploit the reduced space of C. elegans postures to develop a novel tracking algorithm which captures both simple shapes and also self-occluding coils, an important, yet unexplored, component of worm behavior. We apply our algorithm to show that visually ... More

Performance analysis of polling systems with retrials and glue periodsOct 19 2016We consider gated polling systems with two special features: (i) retrials, and (ii) glue or reservation periods. When a type-$i$ customer arrives, or retries, during a glue period of station $i$, it will be served in the next visit period of the server ... More

Simulating stellar winds in AMUSEMar 26 2019We present stellar_wind.py, a module that provides multiple methods of simulating stellar winds using smoothed particle hydrodynamics codes (SPH) within the astrophysical multipurpose software environment (AMUSE) framework. With the simple wind mode, ... More

On the Scalability and Message Count of Trickle-based Broadcasting SchemesSep 29 2015As the use of wireless sensor networks increases, the need for efficient and reliable broadcasting algorithms grows. Ideally, a broadcasting algorithm should have the ability to quickly disseminate data, while keeping the number of transmissions low. ... More

Carbon-enhanced metal-poor stars and thermohaline mixingFeb 06 2007One possible scenario for the formation of carbon-enhanced metal-poor stars is the accretion of carbon-rich material from a binary companion which may no longer visible. It is generally assumed that the accreted material remains on the surface of the ... More

The occurrence of nitrogen-enhanced metal-poor stars: implications for the initial mass function in the early Galactic haloSep 26 2012Most carbon-enhanced metal-poor (CEMP) stars are thought to result from past mass transfer of He-burning material from an asymptotic giant branch (AGB) star to a low-mass companion star, which we now observe as a CEMP star. Because AGB stars of intermediate ... More

A Complete N-body Model of the Old Open Cluster M67Jul 11 2005The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here we present ... More

Variational inference for neural network matrix factorization and its application to stochastic blockmodelingMay 11 2019Jun 09 2019We consider the probabilistic analogue to neural network matrix factorization (Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and fit with variational inference. We find that a linear model fit with variational inference can ... More

Direct N-body Modelling of Stellar Populations: Blue Stragglers in M67Dec 05 2000We present a state-of-the-art N-body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar ... More

Could Edge-Lit Type Ia Supernovae be Standard CandlesDec 14 2001Oct 23 2002The progenitors of Type Ia supernovae (SNe Ia) have not been identified. Though they are no longer fashionable we investigate the consequences if a significant number of SNe Ia were edge-lit detonations (ELDs) of carbon/oxygen white dwarfs that have accreted ... More

Revenue Maximization in an Optical Router Node Using Multiple WavelengthsSep 15 2018In this paper, an optical router node with multiple wavelengths is considered. We introduce revenue for successful transmission and study the ensuing revenue maximization problem. We present an efficient and accurate heuristic procedure for solving the ... More

Data Dissemination Performance in Large-Scale Sensor NetworksJul 22 2014As the use of wireless sensor networks increases, the need for (energy-)efficient and reliable broadcasting algorithms grows. Ideally, a broadcasting algorithm should have the ability to quickly disseminate data, while keeping the number of transmissions ... More

Massive Binary Stars and Self-Enrichment of Globular ClustersFeb 04 2013Globular clusters contain many stars with surface abundance patterns indicating contributions from hydrogen burning products, as seen in the anti-correlated elemental abundances of e.g. sodium and oxygen, and magnesium and aluminium. Multiple generations ... More

Orbital properties of binary post-AGB starsOct 03 2018Oct 08 2018Binary post-asymptotic giant branch (post-AGB) stars are thought to be the products of a strong but poorly-understood interaction during the AGB phase. The aim of this contribution is to update the orbital elements of a sample of galactic post-AGB binaries ... More

Binary white dwarfs in the halo of the Milky WayJul 09 2014Sep 02 2014Aims: We study single and binary white dwarfs in the inner halo of the Milky Way in order to learn more about the conditions under which the population of halo stars was born, such as the initial mass function (IMF), the star formation history, or the ... More

Convection in a Single Column -- Modelling, Algorithm and AnalysisAug 18 2016The group focused on a model problem of idealised moist air convection in a single column of atmosphere. Height, temperature and moisture variables were chosen to simplify the mathematical representation (along the lines of the Boussinesq approximation ... More

MODEST-1: Integrating Stellar Evolution and Stellar DynamicsJul 15 2002Nov 01 2002We summarize the main results from MODEST-1, the first workshop on MOdeling DEnse STellar systems. Our goal is to go beyond traditional population synthesis models, by introducing dynamical interactions between single stars, binaries, and multiple systems. ... More

Assessment of cortical reorganization and preserved function in phantom limb pain: a methodological perspectiveFeb 19 2019Phantom limb pain (PLP) has been associated with both the reorganization of the somatotopic map in primary somatosensory cortex (S1) and preserved S1 function. Here we assessed the nature of the information (sensory, motor) that reaches S1 and methodological ... More

Origin of central abundances in the hot intra-cluster medium - II. Chemical enrichment and supernova yield modelsAug 12 2016The hot intra-cluster medium (ICM) is rich in metals, which are synthesised by supernovae (SNe) and accumulate over time into the deep gravitational potential well of clusters of galaxies. Since most of the elements visible in X-rays are formed by type ... More