arXiv subjects

Michael Schmidt

Publications and source records attributed to Michael Schmidt.

At least 55 records · Page 3Linked to original sources

arXiv2021

Graph? Yes! Which one? Help!

Amazon Neptune is a graph database service that supports two graph (meta)models: W3C's Resource Description Framework (RDF) and Labeled Property Graphs (LPG). Customers opt in for one or the other model, and this choice determines which data modeling features can be used, and - perhaps more importantly - which query languages are available to query and manipulate the graph. The choice between the two technology stacks is difficult and requires consideration of data modeling aspects, query language features, their adequacy for current and future use cases, as well as many other factors (including developer preferences). Sometimes we see customers make the wrong choice with no easy way to reverse it later. It is therefore highly desirable that the choice of the query language can be made without consideration of what graph model is chosen, and can be easily revised or complemented at a later point. In this paper, we advocate and explore the idea of a single, unified graph data model that embraces both RDF and LPGs, and naturally supports different graph query languages on top. We investigate obstacles towards unifying the two graph data models, and propose an initial unifying model, dubbed "one graph" ("1G" for short), as the basis for moving forward.

cs.DB↗

arXiv2020

Mt. Wendelstein imaging of comet 41P/Tuttle-Giacobini-Kresak during the 2017 perihelion arc

Comet 41P/Tuttle-Giacobini-Kresak (41P), a Jupiter family comet with three discoveries over about 100 years, is in a short-periodic orbit around the Sun with the perihelion close to the Earth distance. The 2017 apparition of 41P offered a long-lasting visibility of the comet at a close distance to Earth. The four month-long imaging campaign with the 2 m telescope at the Mount Wendelstein Observatory was aimed at characterizing dust activity and nucleus properties of the comet. Using a new analysis method of the inner coma flux, we derived a small mean equivalent radius of about 600 m for the nucleus with an unusual body axes ratio that is higher than two. The nucleus rotation axis was determined from the geometric appearance of coma structures, which were enhanced in the images. A long-lasting coma fan was produced by an extended region at high latitudes on the slowly rotating nucleus, whereas isolated jets originated from narrow, low latitude active regions on the nucleus. The dust activity of 41P, despite being difficult to quantify exactly because of an unknown phase function correction for the comet, indicates a steep radial profile that falls off with an increasing distance from the Sun. Colors and flux profiles provide evidence for dust fragmentation in the inner coma of the comet. A singular outburst event created various dust structures in the coma. The outburst came from an extended region on the nucleus and was due to either a landslide on the nucleus or a sudden material release from a subsurface pocket of volatile ice.

astro-ph.EP↗

arXiv2019

Scalable Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data

Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if data is incomplete, the latent states of the CTBN have to be estimated by laboriously simulating the intractable dynamics of the assumed CTBN. This is a problem, especially for structure learning tasks, where this has to be done for each element of a super-exponentially growing set of possible structures. In order to circumvent this notorious bottleneck, we develop a novel gradient-based approach to structure learning. Instead of sampling and scoring all possible structures individually, we assume the generator of the CTBN to be composed as a mixture of generators stemming from different structures. In this framework, structure learning can be performed via a gradient-based optimization of mixture weights. We combine this approach with a new variational method that allows for a closed-form calculation of this mixture marginal likelihood. We show the scalability of our method by learning structures of previously inaccessible sizes from synthetic and real-world data.

stat.ML↗

arXiv2019

Entropy: The former trouble with particles (including a new numerical model computational penalty for the Akaike information criterion)

Traditional random-walk particle-tracking (PT) models of advection and dispersion do not track entropy, because particle masses remain constant. Newer mass-transfer particle tracking (MTPT) models have the ability to do so because masses of all compounds may change along trajectories. Additionally, the probability mass functions (PMF) of these MTPT models may be compared to continuous solutions with probability density functions, when a consistent definition of entropy (or similarly, the dilution index) is constructed. This definition reveals that every numerical model incurs a computational entropy. Similar to Akaike's entropic penalty for larger numbers of adjustable parameters, the computational complexity of a model (e.g., number of nodes) adds to the entropy and, as such, must be penalized. The MTPT method can use a particle-collision based kernel or an SPH-derived adaptive kernel. The latter is more representative of a locally well-mixed system (i.e., one in which the dispersion tensor equally represents mixing and solute spreading), while the former better represents the separate processes of mixing versus spreading. We use computational means to demonstrate the viability of each of these methods.

physics.comp-ph↗

arXiv2018

The Wendelstein Weak Lensing (WWL) pathfinder: Accurate weak lensing masses for Planck clusters

We present results from the Wendelstein Weak Lensing (WWL) pathfinder project, in which we have observed three intermediate redshift Planck clusters of galaxies with the new 30'$\times 30$' wide field imager at the 2m Fraunhofer Telescope at Wendelstein Observatory. We investigate the presence of biases in our shear catalogues and estimate their impact on our weak lensing mass estimates. The overall calibration uncertainty depends on the cluster redshift and is below 8.1-15 per cent for $z \approx 0.27-0.77$. It will decrease with improvements on the background sample selection and the multiplicative shear bias calibration. We present the first weak lensing mass estimates for PSZ1 G109.88+27.94 and PSZ1 G139.61+24.20, two SZ-selected cluster candidates. Based on Wendelstein colors and SDSS photometry, we find that the redshift of PSZ1 G109.88+27.94 has to be corrected to $z \approx 0.77$. We investigate the influence of line-of-sight structures on the weak lensing mass estimates and find upper limits for two groups in each of the fields of PSZ1 G109.88+27.94 and PSZ1 G186.98+38.66. We compare our results to SZ and dynamical mass estimates from the literature, and in the case of PSZ1 G186.98+38.66 to previous weak lensing mass estimates. We conclude that our pathfinder project demonstrates that weak lensing cluster masses can be accurately measured with the 2m Fraunhofer Telescope.

astro-ph.CO↗

arXiv2017

Four-dimensional light shaping: manipulating ultrafast spatio-temporal foci in space and time

Spectral dispersion of ultrashort pulses allows simultaneous focusing of light in both space and time creating so-called spatio-temporal foci. Such space-time coupling may be combined with existing holographic techniques to give a further dimension of control when generating focal light fields. It is shown that a phase-only hologram placed in the pupil plane of an objective and illuminated by a spatially chirped ultrashort pulse can be used to generate three dimensional arrays of spatio-temporally focused spots. Exploiting the pulse front tilt generated at focus when applying simultaneous spatial and temporal focusing (SSTF), it is possible to overlap neighbouring foci in time to create a smooth intensity distribution. The resulting light field displays a high level of axial confinement, with experimental demonstrations given through two-photon microscopy and non-linear laser fabrication of glass.

physics.optics↗

arXiv2017

A Kernel-based Lagrangian Method for Imperfectly-mixed Chemical Reactions

Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of particles is tied to the statistics of the initial concentration fields of the system at hand. Systems with shorter-range correlation and/or smaller concentration variance require more particles, potentially limiting the computational feasibility of the method. For the well-known problem of bimolecular reaction, we show that using kernel-based, rather than Dirac-delta, particles can significantly reduce the required number of particles. We derive the fixed width of a Gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and Dirac solutions at any specified time. We also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval. Numerical results show that the width of the kernel should be kept below about 12% of the domain size, and that the analytic equations used to derive kernel width suffer significantly from the neglect of higher-order moments. The simulations with a kernel width given by least squares minimization perform better than those made to match at one specific time. A heuristic time-variable kernel size, based on the previous results, performs on a par with the least squares fixed kernel size.

math.NA↗

arXiv2016

Mt. Wendelstein Imaging of the Post-Perihelion Dust Coma of 67P/Churyumov-Gerasimenko in 2015/2016

Comet 67P/Churyumov-Gerasimenko (67P) was imaged with the 2m telescope at Mt. Wendelstein Observatory in the Alps. Coma and tail monitoring was performed during 51 nights between 22 August 2015 and 9 May 2016. The images through r and i Sloan Digital Sky Survey (SDSS) filters show the dust distribution around the comet, while images in the SDSS g filter indicate also the presence of coma gas in early September 2015. The dust color of 67P implies intrinsic reddening of 9 %/100nm. After maximum shortly after perihelion passage the dust activity decreased with a heliocentric exponent of 4.1 to 4.2 from late September 2015 until May 2016. The opposition surge during early 2016 can be explained by a linear light scattering phase function (beta ~ 0.04) or an asteroid-like HG-type phase function (G ~ 0.15). The radial brightness profile indicates a 'quasi-steady-state' dust coma from late September to the end of 2015. Dust fragmentation during about a month after perihelion may be responsible for radial coma profiles with slopes below unity, while dust accumulation due to very slow dust expansion velocity may result in steeper than unity profiles during 2016. Three fan-shape dust structures are characterized in the coma of 67P. A short dust ejection event on 22 -23 August 2015 has produced a dust arc-let and jet feature in the coma. In September 2015 the appearance of cometary dust tail is dominated by young dust produced around perihelion. The older dust dominates the tail appearance as of mid November 2015.

astro-ph.EP↗

arXiv2013

Pleasantly Consuming Linked Data with RDF Data Descriptions

Although the intention of RDF is to provide an open, minimally constraining way for representing information, there exists an increasing number of applications for which guarantees on the structure and values of an RDF data set become desirable if not essential. What is missing in this respect are mechanisms to tie RDF data to quality guarantees akin to schemata of relational databases, or DTDs in XML, in particular when translating legacy data coming with a rich set of integrity constraints - like keys or cardinality restrictions - into RDF. Addressing this shortcoming, we present the RDF Data Description language (RDD), which makes it possible to specify instance-level data constraints over RDF. Making such constraints explicit does not only help in asserting and maintaining data quality, but also opens up new optimization opportunities for query engines and, most importantly, makes query formulation a lot easier for users and system developers. We present design goals, syntax, and a formal, First-order logics based semantics of RDDs and discuss the impact on consuming Linked Data.

cs.DB↗

arXiv2013

Optomechanical Metamaterials: Dirac polaritons, Gauge fields, and Instabilities

Freestanding photonic crystals can be used to trap both light and mechanical vibrations. These "optomechanical crystal" structures have already been experimentally demonstrated to yield strong coupling between a photon mode and a phonon mode, co-localized at a single defect site. Future devices may feature a regular superlattice of such defects, turning them into "optomechanical arrays". In this letter we predict that tailoring the optomechanical band structure of such arrays can be used to implement Dirac physics of photons and phonons, to create a photonic gauge field via mechanical vibrations, and to observe a novel optomechanical instability.

physics.optics↗

arXiv2012

Optomechanical circuits for nanomechanical continuous variable quantum state processing

We propose and analyze a nanomechanical architecture where light is used to perform linear quantum operations on a set of many vibrational modes. Suitable amplitude modulation of a single laser beam is shown to generate squeezing, entanglement, and state-transfer between modes that are selected according to their mechanical oscillation frequency. Current optomechanical devices based on photonic crystals may provide a platform for realizing this scheme.

cond-mat.mes-hall↗

arXiv2012

An Experience Report of Large Scale Federations

We present an experimental study of large-scale RDF federations on top of the Bio2RDF data sources, involving 29 data sets with more than four billion RDF triples deployed in a local federation. Our federation is driven by FedX, a highly optimized federation mediator for Linked Data. We discuss design decisions, technical aspects, and experiences made in setting up and optimizing the Bio2RDF federation, and present an exhaustive experimental evaluation of the federation scenario. In addition to a controlled setting with local federation members, we study implications arising in a hybrid setting, where local federation members interact with remote federation members exhibiting higher network latency. The outcome demonstrates the feasibility of federated semantic data management in general and indicates remaining bottlenecks and research opportunities that shall serve as a guideline for future work in the area of federated semantic data processing.

cs.DB↗

arXiv2012

A Tale of Two Arc Lengths: Metric notions for curves in surfaces in equiaffine space

In Euclidean geometry, all metric notions (arc length for curves, the first fundamental form for surfaces, etc.) are derived from the Euclidean inner product on tangent vectors, and this inner product is preserved by the full symmetry group of Euclidean space (translations, rotations, and reflections). In equiaffine geometry, there is no invariant notion of inner product on tangent vectors that is preserved by the full equiaffine symmetry group. Nevertheless, it is possible to define an invariant notion of arc length for nondegenerate curves, and an invariant first fundamental form for nondegenerate surfaces in equiaffine space. This leads to two possible notions of arc length for a curve contained in a surface, and these two arc length functions do not necessarily agree. In this paper we will derive necessary and sufficient conditions under which the two arc length functions do agree, and illustrate with examples.

math.DG↗

arXiv2011

Population physiology: leveraging population scale (EHR) data to understand human endocrine dynamics

Studying physiology over a broad population for long periods of time is difficult primarily because collecting human physiologic data is intrusive, dangerous, and expensive. Electronic health record (EHR) data promise to support the development and testing of mechanistic physiologic models on diverse population, but limitations in the data have thus far thwarted such use. For instance, using uncontrolled population-scale EHR data to verify the outcome of time dependent behavior of mechanistic, constructive models can be difficult because: (i) aggregation of the population can obscure or generate a signal, (ii) there is often no control population, and (iii) diversity in how the population is measured can make the data difficult to fit into conventional analysis techniques. This paper shows that it is possible to use EHR data to test a physiological model for a population and over long time scales. Specifically, a methodology is developed and demonstrated for testing a mechanistic, time-dependent, physiological model of serum glucose dynamics with uncontrolled, population-scale, physiological patient data extracted from an EHR repository. It is shown that there is no observable daily variation the normalized mean glucose for any EHR subpopulations. In contrast, a derived value, daily variation in nonlinear correlation quantified by the time-delayed mutual information (TDMI), did reveal the intuitively expected diurnal variation in glucose levels amongst a wild population of humans. Moreover, in a population of intravenously fed patients, there was no observable TDMI-based diurnal signal. These TDMI-based signals, via a glucose insulin model, were then connected with human feeding patterns. In particular, a constructive physiological model was shown to correctly predict the difference between the general uncontrolled population and a subpopulation whose feeding was controlled.

q-bio.QM↗

arXiv2009

On Chase Termination Beyond Stratification

We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data integration. The basic idea of the chase is, given a database instance and a set of constraints as input, to fix constraint violations in the database instance. It is well-known that, for an arbitrary set of constraints, the chase does not necessarily terminate (in general, it is even undecidable if it does or not). Addressing this issue, we review the limitations of existing sufficient termination conditions for the chase and develop new techniques that allow us to establish weaker sufficient conditions. In particular, we introduce two novel termination conditions called safety and inductive restriction, and use them to define the so-called T-hierarchy of termination conditions. We then study the interrelations of our termination conditions with previous conditions and the complexity of checking our conditions. This analysis leads to an algorithm that checks membership in a level of the T-hierarchy and accounts for the complexity of termination conditions. As another contribution, we study the problem of data-dependent chase termination and present sufficient termination conditions w.r.t. fixed instances. They might guarantee termination although the chase does not terminate in the general case. As an application of our techniques beyond those already mentioned, we transfer our results into the field of query answering over knowledge bases where the chase on the underlying database may not terminate, making existing algorithms applicable to broader classes of constraints.

cs.DB↗

arXiv2009

Stop the Chase

The chase procedure, an algorithm proposed 25+ years ago to fix constraint violations in database instances, has been successfully applied in a variety of contexts, such as query optimization, data exchange, and data integration. Its practicability, however, is limited by the fact that - for an arbitrary set of constraints - it might not terminate; even worse, chase termination is an undecidable problem in general. In response, the database community has proposed sufficient restrictions on top of the constraints that guarantee chase termination on any database instance. In this paper, we propose a novel sufficient termination condition, called inductive restriction, which strictly generalizes previous conditions, but can be checked as efficiently. Furthermore, we motivate and study the problem of data-dependent chase termination and, as a key result, present sufficient termination conditions w.r.t. fixed instances. They are strictly more general than inductive restriction and might guarantee termination although the chase does not terminate in the general case.

cs.DB↗

arXiv2009

Foundations of SPARQL Query Optimization

The SPARQL query language is a recent W3C standard for processing RDF data, a format that has been developed to encode information in a machine-readable way. We investigate the foundations of SPARQL query optimization and (a) provide novel complexity results for the SPARQL evaluation problem, showing that the main source of complexity is operator OPTIONAL alone; (b) propose a comprehensive set of algebraic query rewriting rules; (c) present a framework for constraint-based SPARQL optimization based upon the well-known chase procedure for Conjunctive Query minimization. In this line, we develop two novel termination conditions for the chase. They subsume the strongest conditions known so far and do not increase the complexity of the recognition problem, thus making a larger class of both Conjunctive and SPARQL queries amenable to constraint-based optimization. Our results are of immediate practical interest and might empower any SPARQL query optimizer.

cs.DB↗

arXiv2008

SP2Bench: A SPARQL Performance Benchmark

Recently, the SPARQL query language for RDF has reached the W3C recommendation status. In response to this emerging standard, the database community is currently exploring efficient storage techniques for RDF data and evaluation strategies for SPARQL queries. A meaningful analysis and comparison of these approaches necessitates a comprehensive and universal benchmark platform. To this end, we have developed SP^2Bench, a publicly available, language-specific SPARQL performance benchmark. SP^2Bench is settled in the DBLP scenario and comprises both a data generator for creating arbitrarily large DBLP-like documents and a set of carefully designed benchmark queries. The generated documents mirror key characteristics and social-world distributions encountered in the original DBLP data set, while the queries implement meaningful requests on top of this data, covering a variety of SPARQL operator constellations and RDF access patterns. As a proof of concept, we apply SP^2Bench to existing engines and discuss their strengths and weaknesses that follow immediately from the benchmark results.

cs.DB↗