Complexity of checking whether two automata are synchronized by the same language

A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.Comment: 12 pages, 4 figure

Etch Induced Microwave Losses in Titanium Nitride Superconducting Resonators

We have investigated the correlation between the microwave loss and patterning method for coplanar waveguide titanium nitride resonators fabricated on Si wafers. Three different methods were investigated: fluorine- and chlorine-based reactive ion etches and an argon-ion mill. At high microwave probe powers the reactive etched resonators showed low internal loss, whereas the ion-milled samples showed dramatically higher loss. At single-photon powers we found that the fluorine-etched resonators exhibited substantially lower loss than the chlorine-etched ones. We interpret the results by use of numerically calculated filling factors and find that the silicon surface exhibits a higher loss when chlorine-etched than when fluorine-etched. We also find from microscopy that re-deposition of silicon onto the photoresist and side walls is the probable cause for the high loss observed for the ion-milled resonator

Navigability is a Robust Property

The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions

Validation of the effect of cross-calibrated GOES solar proton effective energies on derived integral fluxes by comparison with STEREO observations

The derivation of integral fluxes from instrument coincidence rates requires accurate knowledge of their effective energies. Recent cross calibrations of GOES with the high-energy-resolution Interplanetary Monitoring Platform (IMP) 8 Goddard Medium Energy Experiment (GME) (Sandberg et al., Geophys. Res. Lett, 41, 4435, 2014a) gave significantly lower effective energies than those currently used by the NOAA Space Weather Prediction Center to calculate solar proton integral fluxes from GOES rates. This implies systematically lower integral fluxes than currently produced. This paper quantifies the differences between the current and the cross-calibrated GOES integral fluxes and validates the latter. Care is taken to rule out the spectral resolution of the measurements or different integration algorithms as major contributors to differences in the magnitudes of the derived integral fluxes. The lower effective energies are validated by comparison with the independent, high-resolution observations by the STEREO Low-Energy Telescope (LET) and High-Energy Telescope (HET) during the December 2006 solar proton events. The current GOES product is similar to the >10 MeV integral fluxes recalculated by using the Sandberg et al. [2014a] effective energies but is substantially greater at higher energies. (The median ratios of the current to the recalculated fluxes are 1.1 at >10 MeV, 1.7 at >30 MeV, 2.1 at >60 MeV, and 2.9 at >100 MeV.) By virtue of this validation, the cross-calibrated GOES integral fluxes should be considered more accurate than the current NOAA product. The results of this study also demonstrate good consistency between the two long-term IMP 8 GME and STEREO LET and HET solar proton data sets

Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

The Los Alamos Trapped Ion Quantum Computer Experiment

The development and theory of an experiment to investigate quantum computation with trapped calcium ions is described. The ion trap, laser and ion requirements are determined, and the parameters required for quantum logic operations as well as simple quantum factoring are described.Comment: 41 pages, 16 figures, submitted to Fortschritte der Physi

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

A titanium-nitride near-infrared kinetic inductance photon-counting detector and its anomalous electrodynamics

We demonstrate single-photon counting at 1550 nm with titanium-nitride (TiN) microwave kinetic inductance detectors. Energy resolution of 0.4 eV and arrival-time resolution of 1.2 microseconds are achieved. 0-, 1-, 2-photon events are resolved and shown to follow Poisson statistics. We find that the temperature-dependent frequency shift deviates from the Mattis-Bardeen theory, and the dissipation response shows a shorter decay time than the frequency response at low temperatures. We suggest that the observed anomalous electrodynamics may be related to quasiparticle traps or subgap states in the disordered TiN films. Finally, the electron density-of-states is derived from the pulse response.Comment: 4 pages, 3 figure

Observation of power-law scaling for phase transitions in linear trapped ion crystals

We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to 10 ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.Comment: Physical Review Letters in press, 4 pages, 4 figure