Sangaku in Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid

When the country of Japan was closed from the rest of the world from 1603 until1867 during the Edo period, the field of mathematics developed in a different wayfrom how it developed in the rest of the world. One way we see this developmentis through the sangaku, the thousands of geometric problems hung in various Shinto and Buddhist temples throughout the country. Written on wooden tablets by people from numerous walks of life, all these problems hold true within Euclidean geometry. During the 1800s, while Japan was still closed, non-Euclidean geometries began to develop across the globe, so the isolated nation was entirely unaware of these new systems. Thus, we will explore the sangaku in two of the other well-known systems, namely the neutral and hyperbolic geometric systems. Specifically, we will highlight how these traditionally-solved problems change under the varying definitions of line parallelism

Kōlams in Graph Theory: Mathematics in South Indian Ritual Art

Kōlams are a ritual art form found in India, most commonly in the southern stateof Tamil Nadu. Comprised of different interlocking knots, these women-drawn designs are placed on the entrances to people’s home to showcase the household’s emotional state and ask the earth goddess Bhūdevi for forgiveness. More aesthetically pleasing kōlams are considered latshanam, where the design permeates beauty; monolinearity is one such aspect that implements latshanam. Using graph theory, we examine one style of these drawings, the labyrinthine variety, to identify if a given kōlam is monolinear and how to construct monolinear kōlams

Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases

The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data to reduce measurement and computational costs of detecting non-local quantum correlations. The tolerance of errors due to decoherence and gate infidelities is a key requirement for the application of quantum neural networks on near-term quantum computers. Here we construct quantum convolutional neural networks (QCNNs) that can, in the presence of incoherent errors, recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians from one another as well as from topologically trivial phases. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-breaking errors below a threshold error probability and against all symmetry-preserving errors provided the error channel is invertible. This is in contrast to string order parameters and the output of previously designed QCNNs, which vanish in the presence of any symmetry-breaking errors. To facilitate the implementation of the QCNNs on near-term quantum computers, the QCNN circuits can be shortened from logarithmic to constant depth in system size by performing a large part of the computation in classical post-processing. These constant-depth QCNNs reduce sample complexity exponentially with system size in comparison to the direct sampling using local Pauli measurements.Comment: 24 pages, 12 figure

Automobile Seat Comfort

Johnson Controlshttp://deepblue.lib.umich.edu/bitstream/2027.42/96204/1/me450f12project11_report.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96204/2/me450f12project11_photo.jp

A Lightweight Regression Method to Infer Psycholinguistic Properties for Brazilian Portuguese

Psycholinguistic properties of words have been used in various approaches to Natural Language Processing tasks, such as text simplification and readability assessment. Most of these properties are subjective, involving costly and time-consuming surveys to be gathered. Recent approaches use the limited datasets of psycholinguistic properties to extend them automatically to large lexicons. However, some of the resources used by such approaches are not available to most languages. This study presents a method to infer psycholinguistic properties for Brazilian Portuguese (BP) using regressors built with a light set of features usually available for less resourced languages: word length, frequency lists, lexical databases composed of school dictionaries and word embedding models. The correlations between the properties inferred are close to those obtained by related works. The resulting resource contains 26,874 words in BP annotated with concreteness, age of acquisition, imageability and subjective frequency.Comment: Paper accepted for TSD201

Distribution of H-alpha Emitters in Merging Galaxy Clusters

Studies of star formation in various galaxy cluster mergers have reached apparently contradictory conclusions regarding whether mergers stimulate star formation, quench it, or have no effect. Because the mergers studied span a range of time since pericenter (TSP), it is possible that the apparent effect on star formation is a function of TSP. We use a sample of 12 bimodal mergers to assess the star formation as a function of TSP. We measure the equivalent width of the H-alpha emission line in ${\sim}100$ member galaxies in each merger, classify galaxies as emitters or non-emitters, and then classify emitters as star-forming galaxies (SFG) or active galactic nucleus (AGN) based on the [NII] $\lambda6583$ line. We quantify the distribution of SFG and AGN relative to non-emitters along the spatial axis defined by the subcluster separation. The SFG and AGN fractions vary from merger to merger, but show no trend with TSP. The spatial distribution of SFG is consistent with that of non-emitters in eight mergers, but show significant avoidance of the system center in the remaining four mergers, including the three with the lowest TSP. If there is a connection between star formation activity and TSP, probing it further will require more precise TSP estimates and more mergers with TSP in the range of 0-400 Myr.Comment: accepted to A

Top-Down Modulation of the Auditory Steady-State Response in a Task-Switch Paradigm

Auditory selective attention is an important mechanism for top-down selection of the vast amount of auditory information our perceptual system is exposed to. In the present study, the impact of attention on auditory steady-state responses is investigated. This issue is still a matter of debate and recent findings point to a complex pattern of attentional effects on the auditory steady state response (aSSR). The present study aimed at shedding light on the involvement of ipsilateral and contralateral activations to the attended sound taking into account hemispheric differences and a possible dependency on modulation frequency. In aid of this, a dichotic listening experiment was designed using amplitude-modulated tones that were presented to the left and right ear simultaneously. Participants had to detect target tones in a cued ear while their brain activity was assessed using MEG. Thereby, a modulation of the aSSR by attention could be revealed, interestingly restricted to the left hemisphere and 20 Hz responses: contralateral activations were enhanced while ipsilateral activations turned out to be reduced. Thus, our findings support and extend recent findings, showing that auditory attention can influence the aSSR, but only under specific circumstances and in a complex pattern regarding the different effects for ipsilateral and contralateral activations

Using Auditory Steady State Responses to Outline the Functional Connectivity in the Tinnitus Brain

BACKGROUND: Tinnitus is an auditory phantom perception that is most likely generated in the central nervous system. Most of the tinnitus research has concentrated on the auditory system. However, it was suggested recently that also non-auditory structures are involved in a global network that encodes subjective tinnitus. We tested this assumption using auditory steady state responses to entrain the tinnitus network and investigated long-range functional connectivity across various non-auditory brain regions. METHODS AND FINDINGS: Using whole-head magnetoencephalography we investigated cortical connectivity by means of phase synchronization in tinnitus subjects and healthy controls. We found evidence for a deviating pattern of long-range functional connectivity in tinnitus that was strongly correlated with individual ratings of the tinnitus percept. Phase couplings between the anterior cingulum and the right frontal lobe and phase couplings between the anterior cingulum and the right parietal lobe showed significant condition x group interactions and were correlated with the individual tinnitus distress ratings only in the tinnitus condition and not in the control conditions. CONCLUSIONS: To the best of our knowledge this is the first study that demonstrates existence of a global tinnitus network of long-range cortical connections outside the central auditory system. This result extends the current knowledge of how tinnitus is generated in the brain. We propose that this global extend of the tinnitus network is crucial for the continuos perception of the tinnitus tone and a therapeutical intervention that is able to change this network should result in relief of tinnitus