Unsupervised Learning of Invariance Transformations

The need for large amounts of training data in modern machine learning is one of the biggest challenges of the field. Compared to the brain, current artificial algorithms are much less capable of learning invariance transformations and employing them to extrapolate knowledge from small sample sets. It has recently been proposed that the brain might encode perceptual invariances as approximate graph symmetries in the network of synaptic connections. Such symmetries may arise naturally through a biologically plausible process of unsupervised Hebbian learning. In the present paper, we illustrate this proposal on numerical examples, showing that invariance transformations can indeed be recovered from the structure of recurrent synaptic connections which form within a layer of feature detector neurons via a simple Hebbian learning rule. In order to numerically recover the invariance transformations from the resulting recurrent network, we develop a general algorithmic framework for finding approximate graph automorphisms. We discuss how this framework can be used to find approximate automorphisms in weighted graphs in general

Improved Lower Bound for Competitive Graph Exploration

We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the agent has full knowledge of all edges incident to visited vertices, and, in particular, vertices have unique identifiers. Our bound improves a lower bound of 2.5 by Dobrev et al. [SIROCCO'12] and also holds for planar graphs, where it complements an upper bound of 16 by Kalyanasundaram and Pruhs[TCS'94]. The question whether a constant competitive ratio can be achieved in general remains open

The lunar Dhofar 1436 meteorite: ⁴⁰Ar‐ ³⁹Ar chronology and volatiles, revealed by stepwise combustion and crushing methods

The lunar meteorite Dhofar 1436 is dominated by solar wind type noble gases. Solar argon is equilibrated with “parentless” 40Ar commonly known as lunar orphan argon. Ar‐Ar isochron analyses determined the lunar trapped 40Ar/36Ar ratio to 2.51 ± 0.04, yielding a corrected plateau age of 4.1 ± 0.1 Ga, consistent with the lunar Late Heavy Bombardment period. Lunar trapped and radiogenic argon components are all released at high temperatures (1200–1400 °C). Surprisingly, solar noble gases and lunar trapped argon can largely be released by crushing. Initial crushing steps mainly release elementally fractionated solar wind gases, while in advanced crushing steps, cosmogenic components dominate. Cosmogenic noble gases indicate irradiation at the lunar surface; they are less fractionated than solar wind species. We favor a scenario in which both solar and a large fraction of cosmogenic gases were acquired before the 4.1 Ga event, which caused shock metamorphism and formation of the regolith breccia. Sintering and agglutination along grain boundaries resulted in mobilization of solar wind, reimplanted, radiogenic, and cosmogenic noble gases, and resulted in their partial homogenization, fractionation, and retrapping in voids and/or defects accessible by crushing. An alternative scenario would be complete reset of the K‐Ar system 4.1 Ga ago accompanied by loss of all previously accumulated solar and cosmogenic noble gases. Later, the precursor of Dhofar 1436 became lunar regolith and accumulated solar and cosmogenic noble gases and reimplanted 40Ar before its final formation of the polymict impact breccia. The C abundance of the step‐combusted Dhofar 1436 is 555.3 ppm, with δ13C of −28‰ to +11‰. Nitrogen contents released by crushing and combustion are 3.2 ppm and 20.8 ppm, respectively. The lightest nitrogen composition (δ15N = −79‰) is likely due to release from voids of shock metamorphic phases and is rather a result of the mobilization of nitrogen components that accumulated prior to the 4.1 Ga event

3D Ultrasound Computer Tomography for Breast Cancer Diagnosis at KIT: an Overview

3D Ultrasound Computer Tomography (USCT) emitting and receiving spherical wave fronts overcomes the limitations of 2D systems by offering a nearly isotropic 3D point spread function, a large depth of field, less loss of out-of-plane reflections, and fast 3D data acquisition. 3D devices for clinical practice require a more complex hard- and software due to the huge data rate, time-consuming image reconstruction, and large number of small transducers. The here reviewed KIT 3D USCT is a prototype for clinical studies, which realizes for the first time the full benefits of a 3D system

Piezofibre composite transducers for next generation 3D USCT

At the Karlsruhe Institue of Technology (KIT), a 3D-Ultrasound Computer Tomography (3D-USCT) medical imaging system for early breast cancer detection is currently developed. With the next generation of 3D-USCT 2.5, the current region of interest (ROI) of 10 x 10 x 10 cm³ shall be increased to 20 x 20 x 20 cm³ to allow reliable imaging results also for bigger female breasts. Therefore, the opening angle (OA) of the future transducers should be increased to approx. 60 ° at 3 dB while other characteristics such as bandwidth (BW) and resonance frequency should be preserved or even improved. Based on Fraunhofer IKTS Piezofibre composites utilized for transducer production, an optimization is performed on piezoelectric sensor geometry and size, type and structure of matching and backing layer and interconnection technology of the several parts of the transduce

Looking for obscured QSOs in the X-ray emitting ERO population

We present XMM-Newton data centered on one of the MUNICS Near Infrared Cluster Survey fields (S2F1) and we discuss the X-ray properties of the 6 X-ray emitting EROs found. For one of them we have already obtained the redshift using near-infrared spectroscopic data, while for the remaining 5 EROs the analysis is based on photometric redshifts. We find evidence for the presence of an X-ray obscured QSO in at least 5 out of the 6 X-ray emitting EROs. For these 5 objects we derive intrinsic (2-10 keV) luminosities in excess of 10^44 erg/s and intrinsic column densities higher than 10^22 cm^-2. These values have been obtained through a basic X-ray spectral analysis for the three brightest sources and through the analysis of the hardness ratios for the remaining two. All of these 5 X-ray emitting EROs appear extended in the optical/near-infrared bands indicating that the host galaxy emission dominates at these wavelengths. This suggests that the hosted AGNs are likely to be absorbed also in the optical/near-infrared bands: i.e. they are likely X-ray obscured possible type 2 QSOs. For the remaining ERO the presence of an AGN is suggested both by its high 0.5-2 keV luminosity (L(0.5-2 keV)~10^43 erg/s) and by its X-ray-to-optical flux ratio. In this case the quality of the present data prevents us from placing firm constraints on the AGN type hosted. Finally, the near-IR spectrum obtained for one of the 6 EROs classifies the host galaxy as an elliptical at z~1.7 with a stellar mass well in excess of 10^11 M_\odot. This result corroborates the possible link between the QSO activity and the formation of massive spheroids.Comment: Accepted for publication on A&A; 10 pages, 5 figure

On Friedmann's subexponential lower bound for Zadeh's pivot rule

The question whether the Simplex method admits a polynomial time pivot rule remains one of the most important open questions in discrete optimization. Zadeh's pivot rule had long been a promising candidate, before Friedmann (IPCO, 2011) presented a subexponential instance, based on a close relation to policy iteration algorithms for Markov decision processes (MDPs). We investigate Friedmann's lower bound example and exhibit three flaws in the corresponding MDP: We show that (a) the initial policy for the policy iteration does not produce the required occurrence records and improving switches, (b) the specification of occurrence records is not entirely accurate, and (c) the sequence of improving switches used by Friedmann does not consistently follow Zadeh's pivot rule. In this paper, we resolve each of these issues by adapting Friedmann's construction. While the first two issues require only minor changes to the specifications of the initial policy and the occurrence records, the third issue requires a significantly more sophisticated ordering and associated tie-breaking rule that are in accordance with the Least-Entered pivot rule. Most importantly, our changes do not affect the macroscopic structure of Friedmann's MDP, and thus we are able to retain his original result

A hybrid biological neural network model for solving problems in cognitive planning

A variety of behaviors, like spatial navigation or bodily motion, can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of empirical findings about the mammalian neocortex and hippocampus. The neurons and synaptic connections in the model represent structures that can result from self-organization into a cognitive map via Hebbian learning, i.e. into a graph in which each neuron represents a point of some abstract task-relevant manifold and the recurrent connections encode a distance metric on the manifold. Graph traversal problems are solved by wave-like activation patterns which travel through the recurrent network and guide a localized peak of activity onto a path from some starting position to a target state

Piezofibre composite transducers for next generation 3D USCT

At the Karlsruhe Institue of Technology (KIT), a 3D-Ultrasound Computer Tomography (3D-USCT) medical imaging system for early breast cancer detection is currently developed. With the next generation of 3D-USCT 2.5, the current region of interest (ROI) of 10 x 10 x 10 cm³ shall be increased to 20 x 20 x 20 cm³ to allow reliable imaging results also for bigger female breasts. Therefore, the opening angle (OA) of the future transducers should be increased to approx. 60 at 3 dB while other characteristics such as bandwidth (BW) and resonance frequency should be preserved or even improved. Based on Fraunhofer IKTS Piezofibre composites utilized for transducer production, an optimization is performed on piezoelectric sensor geometry and size, type and structure of matching and backing layer and interconnection technology of the several parts of the transducerImPhys/Acoustical Wavefield Imagin