Designing Sparse Reliable Pose-Graph SLAM: A Graph-Theoretic Approach

In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of spanning trees is an open problem in general. To tackle this problem, several new theoretical results are established in this paper, including the monotone log-submodularity of the weighted number of spanning trees. By exploiting these structures, we design a complementary pair of near-optimal efficient approximation algorithms with provable guarantees. Our theoretical results are validated using random graphs and a publicly available pose-graph SLAM dataset.Comment: WAFR 201

Complex Periodic Potentials with a Finite Number of Band Gaps

We obtain several new results for the complex generalized associated Lame potential V(x)= a(a+1)m sn^2(y,m)+ b(b+1)m sn^2(y+K(m),m) + f(f+1)m sn^2(y+K(m)+iK'(m),m)+ g(g+1)m sn^2(y+iK'(m),m), where y = x-K(m)/2-iK'(m)/2, sn(y,m) is a Jacobi elliptic function with modulus parameter m, and there are four real parameters a,b,f,g. First, we derive two new duality relations which, when coupled with a previously obtained duality relation, permit us to relate the band edge eigenstates of the 24 potentials obtained by permutations of the four parameters a,b,f,g. Second, we pose and answer the question: how many independent potentials are there with a finite number "a" of band gaps when a,b,f,g are integers? For these potentials, we clarify the nature of the band edge eigenfunctions. We also obtain several analytic results when at least one of the four parameters is a half-integer. As a by-product, we also obtain new solutions of Heun's differential equation.Comment: 33 pages, 0 figure

One-step-ahead kinematic compressive sensing

A large portion of work on compressive sampling and sensing has focused on reconstructions from a given measurement set. When the individual samples are expensive and optional, as is the case with autonomous agents operating in a physical domain and under specific energy limits, the CS problem takes on a new aspect because the projection is column-sparse, and the number of samples is not necessarily large. As a result, random sampling may no longer be the best tactic. The underlying incoherence properties in l0 reconstruction, however, can still motivate the purposeful design of samples in planning for CS with one or more agents; we develop here a greedy and computationally tractable sampling rule that will improve errors relative to random points. Several example cases illustrate that the approach is effective and robust.United States. Office of Naval Research (Grant N00014-09-1-0700

Correction for Self-Heating When Using Thermometers as Heaters in Precision Control Applications

In precision control applications, thermometers have temperature-dependent electrical resistance with germanium or other semiconductor material thermistors, diodes, metal film and wire, or carbon film resistors. Because resistance readout requires excitation current flowing through the sensor, there is always ohmic heating that leads to a temperature difference between the sensing element and the monitored object. In this work, a thermistor can be operated as a thermometer and a heater, simultaneously, by continuously measuring the excitation current and the corresponding voltage. This work involves a method of temperature readout where the temperature offset due to self-heating is subtracted exactly

The Mid-Infrared Instrument for the James Webb Space Telescope, VII: The MIRI Detectors

The MIRI Si:As IBC detector arrays extend the heritage technology from the Spitzer IRAC arrays to a 1024 x 1024 pixel format. We provide a short discussion of the principles of operation, design, and performance of the individual MIRI detectors, in support of a description of their operation in arrays provided in an accompanying paper (Ressler et al. (2015)). We then describe modeling of their response. We find that electron diffusion is an important component of their performance, although it was omitted in previous models. Our new model will let us optimize the bias voltage while avoiding avalanche gain. It also predicts the fraction of the IR-active layer that is depleted (and thus contributes to the quantum efficiency) as signal is accumulated on the array amplifier. Another set of models accurately predicts the nonlinearity of the detector-amplifier unit and has guided determination of the corrections for nonlinearity. Finally, we discuss how diffraction at the interpixel gaps and total internal reflection can produce the extended cross-like artifacts around images with these arrays at short wavelengths, ~ 5 microns. The modeling of the behavior of these devices is helping optimize how we operate them and also providing inputs to the development of the data pipeline

The Mid-Infrared Instrument for the James Webb Space Telescope, VIII: The MIRI Focal Plane System

We describe the layout and unique features of the focal plane system for MIRI. We begin with the detector array and its readout integrated circuit (combining the amplifier unit cells and the multiplexer), the electronics, and the steps by which the data collection is controlled and the output signals are digitized and delivered to the JWST spacecraft electronics system. We then discuss the operation of this MIRI data system, including detector readout patterns, operation of subarrays, and data formats. Finally, we summarize the performance of the system, including remaining anomalies that need to be corrected in the data pipeline

Magnetic susceptibility of insulators from first principles

We present an {\it ab initio} approach for the computation of the magnetic susceptibility $\chi$ of insulators. The approach is applied to compute $\chi$ in diamond and in solid neon using density functional theory in the local density approximation, obtaining good agreement with experimental data. In solid neon, we predict an observable dependence of $\chi$ upon pressure.Comment: Revtex, to appear in Physical Review Lette

Slowly Rotating Homogeneous Stars and the Heun Equation

The scheme developed by Hartle for describing slowly rotating bodies in 1967 was applied to the simple model of constant density by Chandrasekhar and Miller in 1974. The pivotal equation one has to solve turns out to be one of Heun's equations. After a brief discussion of this equation and the chances of finding a closed form solution, a quickly converging series solution of it is presented. A comparison with numerical solutions of the full Einstein equations allows one to truncate the series at an order appropriate to the slow rotation approximation. The truncated solution is then used to provide explicit expressions for the metric.Comment: 16 pages, uses document class iopart, v2: minor correction

Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation

A hidden nonlinear bosonized supersymmetry was revealed recently in Poschl-Teller and finite-gap Lame systems. In spite of the intimate relationship between the two quantum models, the hidden supersymmetry in them displays essential differences. In particular, the kernel of the supercharges of the Poschl-Teller system, unlike the case of Lame equation, includes nonphysical states. By means of Lame equation, we clarify the nature of these peculiar states, and show that they encode essential information not only on the original hyperbolic Poschl-Teller system, but also on its singular hyperbolic and trigonometric modifications, and reflect the intimate relation of the model to a free particle system.Comment: 10 pages, typos corrected; to appear in J. Phys.

The decay of homogeneous anisotropic turbulence

We present the results of a numerical investigation of three-dimensional decaying turbulence with statistically homogeneous and anisotropic initial conditions. We show that at large times, in the inertial range of scales: (i) isotropic velocity fluctuations decay self-similarly at an algebraic rate which can be obtained by dimensional arguments; (ii) the ratio of anisotropic to isotropic fluctuations of a given intensity falls off in time as a power law, with an exponent approximately independent of the strength of the fluctuation; (iii) the decay of anisotropic fluctuations is not self-similar, their statistics becoming more and more intermittent as time elapses. We also investigate the early stages of the decay. The different short-time behavior observed in two experiments differing by the phase organization of their initial conditions gives a new hunch on the degree of universality of small-scale turbulence statistics, i.e. its independence of the conditions at large scales.Comment: 9 pages, 17 figure