A deep learning approach to diabetic blood glucose prediction

We consider the question of 30-minute prediction of blood glucose levels measured by continuous glucose monitoring devices, using clinical data. While most studies of this nature deal with one patient at a time, we take a certain percentage of patients in the data set as training data, and test on the remainder of the patients; i.e., the machine need not re-calibrate on the new patients in the data set. We demonstrate how deep learning can outperform shallow networks in this example. One novelty is to demonstrate how a parsimonious deep representation can be constructed using domain knowledge

Generic canonical form of pairs of matrices with zeros

We consider a family of pairs of m-by-p and m-by-q matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations (A,B)--> (SAR,SBL) with nonsingular S, R, L. We prove that almost all of these pairs reduce to the same pair (C, D) from this family, except for pairs whose arbitrary entries are zeros of a certain polynomial. The polynomial and the pair (C D) are constructed by a combinatorial method based on properties of a certain graph.Comment: 13 page

Mesoscopic threshold detectors: Telegraphing the size of a fluctuation

We propose a two-terminal method to measure shot noise in mesoscopic systems based on an instability in the current-voltage characteristic of an on-chip detector. The microscopic noise drives the instability, which leads to random switching of the current between two values, the telegraph process. In the Gaussian regime, the shot noise power driving the instability may be extracted from the I-V curve, with the noise power as a fitting parameter. In the threshold regime, the extreme value statistics of the mesoscopic conductor can be extracted from the switching rates, which reorganize the complete information about the current statistics in an indirect way, "telegraphing" the size of a fluctuation. We propose the use of a quantum double dot as a mesoscopic threshold detector.Comment: 9 pages, 7 figures, published versio

Gravitational-Wave Astronomy with Inspiral Signals of Spinning Compact-Object Binaries

Inspiral signals from binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave interferometers (LIGO, Virgo, GEO-600 and TAMA-300). We present parameter-estimation simulations for inspirals of black-hole--neutron-star binaries using Markov-chain Monte-Carlo methods. For the first time, we have both estimated the parameters of a binary inspiral source with a spinning component and determined the accuracy of the parameter estimation, for simulated observations with ground-based gravitational-wave detectors. We demonstrate that we can obtain the distance, sky position, and binary orientation at a higher accuracy than previously suggested in the literature. For an observation of an inspiral with sufficient spin and two or three detectors we find an accuracy in the determination of the sky position of typically a few tens of square degrees.Comment: v2: major conceptual changes, 4 pages, 1 figure, 1 table, submitted to ApJ

Optical spectra of the heavy fermion uniaxial ferromagnet UGe2_2

We report a detailed study of UGe$_{2}$ single crystals using infrared reflectivity and spectroscopic ellipsometry. The optical conductivity suggests the presence of a low frequency interband transition and a narrow free-carrier response with strong frequency dependence of the scattering rate and effective mass. We observe sharp changes in the low frequency mass and scattering rate below the upper ferromagnetic transition $T_C = 53 K$. The characteristic changes are exhibited most strongly at an energy scale of around 12 meV (100 cm$^{-1}$). They recover their unrenormalized value above $T_C$ and for $\omega >$ 40 meV. In contrast no sign of an anomaly is seen at the lower transition temperature of unknown nature $T_x \sim$ 30 K, observed in transport and thermodynamic experiments. In the ferromagnetic state we find signatures of a strong coupling to the longitudinal magnetic excitations that have been proposed to mediate unconventional superconductivity in this compound

Universality check of Abelian Monopoles

We study the Abelian projected SU(2) lattice gauge theory after gauge fixing to the maximally Abelian gauge (MAG). In order to check the universality of the Abelian dominance we employ the tadpole improved tree level (TI) action. We show that the density of monopoles in the largest cluster (the IR component) is finite in the continuum limit which is approximated already at relatively large lattice spacing. The value itself is smaller than in the case of Wilson action. We present results for the ratio of the Abelian to non-Abelian string tension for both Wilson and TI actions for a number of lattice spacings in the range 0.06 fm < a < 0.35 fm. These results show that the ratio is between 0.9 and 0.95 for all considered values of lattice couplings and both actions. We compare the properties of the monopole clusters in two gauges - in MAG and in the Laplacian Abelian gauge (LAG). Whereas in MAG the infrared component of the monopole density shows a good convergence to the continuum limit, we find that in LAG it is even not clear whether a finite limit exists.Comment: 18 pages, 11 figure

Phonon Rabi-assisted tunneling in diatomic molecules

We study electronic transport in diatomic molecules connected to metallic contacts in the regime where both electron-electron and electron-phonon interactions are important. We find that the competition between these interactions results in unique resonant conditions for interlevel transitions and polaron formation: the Coulomb repulsion requires additional energy when electrons attempt phonon-assisted interlevel jumps between fully or partially occupied levels. We apply the equations of motion approach to calculate the electronic Green's functions. The density of states and conductance through the system are shown to exhibit interesting Rabi-like splitting of Coulomb blockade peaks and strong temperature dependence under the it interacting resonant conditions.Comment: Updated version, 5 pages, 4 figures, to be published in Phys. Rev. B on 9/1

Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)

A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1,0,...,0]) of gl(m|n) with highest weight (1,0,. . . ,0) are computed. Both results are steps for the explicit construction of the parastatistics Fock space.Comment: 16 page

The effects of LIGO detector noise on a 15-dimensional Markov-chain Monte-Carlo analysis of gravitational-wave signals

Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo, and GEO-600). We present parameter-estimation results from our Markov-chain Monte-Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals into either synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ("glitch"). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter-estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary.Comment: 11 pages, 2 figures, NRDA09 proceeding