Visualization of AE's Training on Credit Card Transactions with Persistent Homology

Auto-encoders are among the most popular neural network architecture for dimension reduction. They are composed of two parts: the encoder which maps the model distribution to a latent manifold and the decoder which maps the latent manifold to a reconstructed distribution. However, auto-encoders are known to provoke chaotically scattered data distribution in the latent manifold resulting in an incomplete reconstructed distribution. Current distance measures fail to detect this problem because they are not able to acknowledge the shape of the data manifolds, i.e. their topological features, and the scale at which the manifolds should be analyzed. We propose Persistent Homology for Wasserstein Auto-Encoders, called PHom-WAE, a new methodology to assess and measure the data distribution of a generative model. PHom-WAE minimizes the Wasserstein distance between the true distribution and the reconstructed distribution and uses persistent homology, the study of the topological features of a space at different spatial resolutions, to compare the nature of the latent manifold and the reconstructed distribution. Our experiments underline the potential of persistent homology for Wasserstein Auto-Encoders in comparison to Variational Auto-Encoders, another type of generative model. The experiments are conducted on a real-world data set particularly challenging for traditional distance measures and auto-encoders. PHom-WAE is the first methodology to propose a topological distance measure, the bottleneck distance, for Wasserstein Auto-Encoders used to compare decoded samples of high quality in the context of credit card transactions.Comment: arXiv admin note: substantial text overlap with arXiv:1905.0989

Development of silicon carbide semiconductor devices for high temperature applications

The semiconducting properties of electronic grade silicon carbide crystals, such as wide energy bandgap, make it particularly attractive for high temperature applications. Applications for high temperature electronic devices include instrumentation for engines under development, engine control and condition monitoring systems, and power conditioning and control systems for space platforms and satellites. Discrete prototype SiC devices were fabricated and tested at elevated temperatures. Grown p-n junction diodes demonstrated very good rectification characteristics at 870 K. A depletion-mode metal-oxide-semiconductor field-effect transistor was also successfully fabricated and tested at 770 K. While optimization of SiC fabrication processes remain, it is believed that SiC is an enabling high temperature electronic technology

Advances in silicon carbide Chemical Vapor Deposition (CVD) for semiconductor device fabrication

Improved SiC chemical vapor deposition films of both 3C and 6H polytypes were grown on vicinal (0001) 6H-SiC wafers cut from single-crystal boules. These films were produced from silane and propane in hydrogen at one atmosphere at a temperature of 1725 K. Among the more important factors which affected the structure and morphology of the grown films were the tilt angle of the substrate, the polarity of the growth surface, and the pregrowth surface treatment of the substrate. With proper pregrowth surface treatment, 6H films were grown on 6H substrates with tilt angles as small as 0.1 degrees. In addition, 3C could be induced to grow within selected regions on a 6H substrate. The polarity of the substrate was a large factor in the incorporation of dopants during epitaxial growth. A new growth model is discussed which explains the control of SiC polytype in epitaxial growth on vicinal (0001) SiC substrates

Links between particle surface hardening and rehydration impairment during micellar casein powder storage

Storage is an unavoidable critical phase regarding dairy powder reconstitution abilities, particularly for high casein content powders, which generally present a poor rehydration behavior. The ability of micellar casein powders to completely rehydrate can thus be particularly affected by storage time and temperature. To implement best practices for the optimization of storage conditions, understanding changes occurring is a crucial point. For the first time, biophysical techniques were used to investigate powder surface at the nanoscale. Atomic force microscopy revealed that particle surface became rougher during storage, associated with the formation of hollow zones (around 500 nm) holes when stored for 10 months at 40 °C. Mechanical properties of micellar casein particle surface during powder storage was quantified using AFM nanoindentation. Spatially-resolved force/indentation curves evidenced a significant stiffer surface for aged powder (Young modulus of ∼20 GPa) in comparison with the fresh one (∼0.2 GPa). These findings were fully consistent with the formation of a crust at the powder surface observed by high-resolution field-emission scanning electron microscopy during powder rehydration. Finally, alterations of the rehydration process can be related to modifications occurring at the particle surface during storage

Ultracold polar molecules as qudits

We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs, which are examples of molecules with $^2\Sigma$ and $^1\Sigma$ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a 4-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension $d=4$ to perform the Deutsch algorithm

Electronic and Interfacial Properties of PD/6H-SiC Schottky Diode Gas Sensors

Pd/SiC Schottky diodes detect hydrogen and hydrocarbons with high sensitivity. Variation of the diode temperature from 100 C to 200 C shows that the diode sensitivity to propylene is temperature dependent. Long-term heat treating at 425 C up to 140 hours is carried out to determine the effect of extended heat treating on the diode properties and gas sensitivity. The heat treating significantly affects the diode's capacitive characteristics, but the diode's current carrying characteristics are much more stable with a large response to hydrogen. Scanning Electron Microscopy and X-ray Spectrometry studies of the Pd surface after the heating show cluster formation and background regions with grain structure observed in both regions. The Pd and Si concentrations vary between grains. Auger Electron Spectroscopy depth profiles revealed that the heat treating promoted interdiffusion and reaction between the Pd and SiC dw broadened the interface region. This work shows that Pd/SiC Schottky diodes have significant potential as high temperature gas sensors, but stabilization of the structure is necessary to insure their repeatability in long-term, high temperature applications

Efficient intra- and inter-night linking of asteroid detections using kd-trees

The Panoramic Survey Telescope And Rapid Response System (Pan-STARRS) under development at the University of Hawaii's Institute for Astronomy is creating the first fully automated end-to-end Moving Object Processing System (MOPS) in the world. It will be capable of identifying detections of moving objects in our solar system and linking those detections within and between nights, attributing those detections to known objects, calculating initial and differentially-corrected orbits for linked detections, precovering detections when they exist, and orbit identification. Here we describe new kd-tree and variable-tree algorithms that allow fast, efficient, scalable linking of intra and inter-night detections. Using a pseudo-realistic simulation of the Pan-STARRS survey strategy incorporating weather, astrometric accuracy and false detections we have achieved nearly 100% efficiency and accuracy for intra-night linking and nearly 100% efficiency for inter-night linking within a lunation. At realistic sky-plane densities for both real and false detections the intra-night linking of detections into `tracks' currently has an accuracy of 0.3%. Successful tests of the MOPS on real source detections from the Spacewatch asteroid survey indicate that the MOPS is capable of identifying asteroids in real data.Comment: Accepted to Icaru

Nouvelles méthodologies de caractérisation de la réactivité de surface de poudres alimentaires

National audienceCes dernières années, de nombreuses études ont porté sur la caractérisation des propriétés des poudres alimentaires, avec notamment comme objectif la prédiction et le contrôle de ces fonctionnalités. Auparavant, la plupart des études attribuaient les propriétés fonctionnelles à la composition globale de la poudre, alors que de récents travaux ont démontré un lien fort entre fonctionnalités et propriétés de surface. abSTRacT As the food powder production increases more and more it is the time to use new and innovative methodologies to understand the behavior of these powders regarding their functional properties. It was recently demonstrated that many functional properties (such as rehydration, caking, flowability, sticking…) were influenced not only by the particle bulk properties but also the particles surface properties. This chapter presents a number of methodologies in order to better characterize powder particle surfaces. Some of them are now well developed and often used by researchers and food industries. Nevertheless, others are less known but may be very promising in the future. Abréviations : Il semblait donc essentiel de développer de nouvelles méthodologies permettant de caractériser la surface des poudres. C'est ainsi que des approches ont été développées (Figure 1) à différentes échelles d'observation : atomique, moléculaire et microstructurale. A l'échelle atomique, la complémentarité des techniques XPS (Spectroscopie des Photons X) et EDX (Energie Dis-persive des rayons X) s'est révélée intéressante pour sonder la surface des poudres à différentes profondeurs (Figure 2). L'XPS permet ainsi de caractériser la composition atomique de l'extrême surface (≈ 5-10 nm) d'une poudre sur une aire assez importante (700 µm x 300 µm). A l'inverse, l'EDX per-met d'explorer les matrices alimentaires plus en profondeur (≈ 1-5 µm) et sur une surface plus étroite (5 µm²). Il a ainsi été mis en évidence que les poudres laitières, de par leur procédé d'obtention (séchage par atomisation), pré-sentaient des gradients de composition entre la surface et le coeur des particules. D'une manière générale, les protéines et les lipides sont surreprésentés en surface, alors que le lactose et les minéraux sont plutôt localisés au coeur de la particule. En revanche, la surface est plutôt homogène, quelle que soit la zone analysée. De plus, il a été observé une répartition différente des consti-tuants dans les poudres céréalières. Les différences de composition entre surface et coeur des particules sont moins marquées, tandis que la distribution des composants en surface est fortement hétérogène. Figure 1. Approche multi-échelle (de l'atome à la microstructure) permettant de caractériser la surface d'une poudre alimentaire

Failing to hash into supersingular isogeny graphs

An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell$-isogeny graph which does not reveal the endomorphism ring, or a path to a curve of known endomorphism ring. Such a hash function would open up interesting cryptographic applications. In this paper, we document a number of (thus far) failed attempts to solve this problem, in the hope that we may spur further research, and shed light on the challenges and obstacles to this endeavour. The mathematical approaches contained in this article include: (i) iterative root-finding for the supersingular polynomial; (ii) gcd's of specialized modular polynomials; (iii) using division polynomials to create small systems of equations; (iv) taking random walks in the isogeny graph of abelian surfaces; and (v) using quantum random walks.Comment: 33 pages, 7 figure