992 research outputs found
Learning Graphs from Linear Measurements: Fundamental Trade-offs and Applications
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdős-Rényi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n ) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction
A topographic mechanism for arcing of dryland vegetation bands
Banded patterns consisting of alternating bare soil and dense vegetation have
been observed in water-limited ecosystems across the globe, often appearing
along gently sloped terrain with the stripes aligned transverse to the
elevation gradient. In many cases these vegetation bands are arced, with field
observations suggesting a link between the orientation of arcing relative to
the grade and the curvature of the underlying terrain. We modify the water
transport in the Klausmeier model of water-biomass interactions, originally
posed on a uniform hillslope, to qualitatively capture the influence of terrain
curvature on the vegetation patterns. Numerical simulations of this modified
model indicate that the vegetation bands change arcing-direction from
convex-downslope when growing on top of a ridge to convex-upslope when growing
in a valley. This behavior is consistent with observations from remote sensing
data that we present here. Model simulations show further that whether bands
grow on ridges, valleys, or both depends on the precipitation level. A survey
of three banded vegetation sites, each with a different aridity level,
indicates qualitatively similar behavior.Comment: 26 pages, 13 figures, 2 table
Learning Graphs from Linear Measurements: Fundamental Trade-offs and Applications
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdős-Rényi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n ) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction
Learning Graph Parameters from Linear Measurements: Fundamental Trade-offs and Application to Electric Grids
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We study fundamental trade-offs between the number of measurements (sample complexity), the complexity of the graph class, and the probability of error by first deriving a necessary condition (fundamental limit) on the number of measurements. Then, by considering a two-stage recovery scheme, we give a sufficient condition for recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdös-Rényi (n, p) class, the sample complexity derived from the fundamental trade-offs is tight up to multiplicative factors. In addition, we design and implement a polynomial-time (in n) algorithm based on the two-stage recovery scheme. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness of the proposed algorithm for accurate topology and parameter recovery
Learning Graph Parameters from Linear Measurements: Fundamental Trade-offs and Application to Electric Grids
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We study fundamental trade-offs between the number of measurements (sample complexity), the complexity of the graph class, and the probability of error by first deriving a necessary condition (fundamental limit) on the number of measurements. Then, by considering a two-stage recovery scheme, we give a sufficient condition for recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdös-Rényi (n, p) class, the sample complexity derived from the fundamental trade-offs is tight up to multiplicative factors. In addition, we design and implement a polynomial-time (in n) algorithm based on the two-stage recovery scheme. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness of the proposed algorithm for accurate topology and parameter recovery
Tractable Identification of Electric Distribution Networks
The identification of distribution network topology and parameters is a
critical problem that lays the foundation for improving network efficiency,
enhancing reliability, and increasing its capacity to host distributed energy
resources. Network identification problems often involve estimating a large
number of parameters based on highly correlated measurements, resulting in an
ill-conditioned and computationally demanding estimation process. We address
these challenges by proposing two admittance matrix estimation methods. In the
first method, we use the eigendecomposition of the admittance matrix to
generalize the notion of stationarity to electrical signals and demonstrate how
the stationarity property can be used to facilitate a maximum a posteriori
estimation procedure. We relax the stationarity assumption in the second
proposed method by employing Linear Minimum Mean Square Error (LMMSE)
estimation. Since LMMSE estimation is often ill-conditioned, we introduce an
approximate well-conditioned solution based on eigenvalue truncation. Our
quantitative results demonstrate the improvement in computational efficiency
compared to the state-of-the-art methods while preserving the estimation
accuracy
Nonlinear Qubit Transformations
We generalise our previous results of universal linear manipulations [Phys.
Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit
transformations using measurement and quantum based schemes. Firstly, nonlinear
rotations are studied. We rotate different parts of a Bloch sphere in opposite
directions about the z-axis. The second transformation is a map which sends a
qubit to its orthogonal state (which we define as ORTHOG). We consider the case
when the ORTHOG is applied to only a partial area of a Bloch sphere. We also
study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi),
again, applied only to part of the Bloch sphere. In order to achieve these
three operations, we consider different measurement preparations and derive the
optimal average (instead of universal) quantum unitary transformations. We also
introduce a simple method for a qubit measurement and its application to other
cases.Comment: minor corrections. To appear in PR
Representations and concepts of professional ethos among Swiss religious education teacher trainers
Over the past two decades, the organisation of religious education classes in Switzerland has undergone profound reforms. Amid the increasing secularisation and pluralisation of the religious landscape, many cantons have introduced a compulsory course that falls under the responsibility of the state and is aimed at teaching basic knowledge about a variety of religions. These reforms have enabled a harmonisation of the syllabi for religious education across the country and have prompted the adaptation of teacher training programmes. Because of the many diverse social expectations surrounding these new courses and the diverse academic tra- ditions in the field of religious education, however, a unified conception of these courses is still absent. In this article, we discuss the ongoing construction of religious education teachers’ professional ethos within this fluid context. In particular, we discuss the perspective of teacher trainers on pragmatic questions concerning religious plurality and the place of teachers’ and pupils’ personal (religious) experiences in the classroom, and pay attention to different representations of ‘religion’ and distinct ideas regarding the purpose of these courses as they have a major impact on the professional attitudes expected from teachers.
Keywords: professional ethos; teacher trainers; Switzerland; concepts of religion; impartialit
A global multiproxy database for temperature reconstructions of the Common Era
Reproducible climate reconstructions of the Common Era (1 CE to present) are
key to placing industrial-era warming into the context of natural climatic
variability. Here we present a community-sourced database of temperature-
sensitive proxy records from the PAGES2k initiative. The database gathers 692
records from 648 locations, including all continental regions and major ocean
basins. The records are from trees, ice, sediment, corals, speleothems,
documentary evidence, and other archives. They range in length from 50 to 2000
years, with a median of 547 years, while temporal resolution ranges from
biweekly to centennial. Nearly half of the proxy time series are significantly
correlated with HadCRUT4.2 surface temperature over the period 1850–2014.
Global temperature composites show a remarkable degree of coherence between
high- and low-resolution archives, with broadly similar patterns across
archive types, terrestrial versus marine locations, and screening criteria.
The database is suited to investigations of global and regional temperature
variability over the Common Era, and is shared in the Linked Paleo Data (LiPD)
format, including serializations in Matlab, R and Python
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