Strong inapproximability of the shortest reset word

The \v{C}ern\'y conjecture states that every $n$-state synchronizing automaton has a reset word of length at most $(n-1)^2$. We study the hardness of finding short reset words. It is known that the exact version of the problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and complete for the DP class, and that approximating the length of the shortest reset word within a factor of $O(\log n)$ is NP-hard [Gerbush and Heeringa, CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly improve on these results by showing that, for every $\epsilon>0$, it is NP-hard to approximate the length of the shortest reset word within a factor of $n^{1-\epsilon}$. This is essentially tight since a simple $O(n)$-approximation algorithm exists.Comment: extended abstract to appear in MFCS 201

Modern Modal Testing: A Cautionary Tale

Over the past 50 years, great advances have been achieved in both analytical modal analysis (i.e. finite element models and analysis) and experimental modal analysis (i.e. modal testing) in aerospace and other fields. With the advent of more powerful computers, higher performance instrumentation and data acquisition systems, and powerful linear modal extraction tools, analysts and test engineers have a breadth and depth of technical resources only dreamed of by our predecessors. However, some observed recent trends indicate that hard lessons learned are being forgotten or ignored, and possibly fundamental concepts are not being understood. These trends have the potential of leading to the degradation of the quality of and confidence in both analytical and test results. These trends are a making of our own doing, and directly related to having ever more powerful computers, programmatic budgetary pressures to limit analysis and testing, and technical capital loss due to the retirement of the senior component of a bimodal workforce. This paper endeavors to highlight some of the most important lessons learned, common pitfalls to hopefully avoid, and potential steps that may be taken to help reverse this trend

Band structure engineering in (Bi1-xSbx)2Te3 ternary topological insulators

Three-dimensional (3D) topological insulators (TI) are novel quantum materials with insulating bulk and topologically protected metallic surfaces with Dirac-like band structure. The spin-helical Dirac surface states are expected to host exotic topological quantum effects and find applications in spintronics and quantum computation. The experimental realization of these ideas requires fabrication of versatile devices based on bulk-insulating TIs with tunable surface states. The main challenge facing the current TI materials exemplified by Bi2Se3 and Bi2Te3 is the significant bulk conduction, which remains unsolved despite extensive efforts involving nanostructuring, chemical doping and electrical gating. Here we report a novel approach for engineering the band structure of TIs by molecular beam epitaxy (MBE) growth of (Bi1-xSbx)2Te3 ternary compounds. Angle-resolved photoemission spectroscopy (ARPES) and transport measurements show that the topological surface states exist over the entire composition range of (Bi1-xSbx)2Te3 (x = 0 to 1), indicating the robustness of bulk Z2 topology. Most remarkably, the systematic band engineering leads to ideal TIs with truly insulating bulk and tunable surface state across the Dirac point that behave like one quarter of graphene. This work demonstrates a new route to achieving intrinsic quantum transport of the topological surface states and designing conceptually new TI devices with well-established semiconductor technology.Comment: Minor changes in title, text and figures. Supplementary information adde

Identification of Ventricular Tachycardia Using Intracardiac Electrograms: A Comparison of Unipolar Versus Bipolar Waveform Analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75535/1/j.1540-8159.1991.tb04091.x.pd

On the interplay between Babai and Černý’s conjectures

Motivated by the Babai conjecture and the Černý conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with n states in this class, we prove that the reset thresholds are upperbounded by 2n2 -6n + 5 and can attain the value (Formula presented). In addition, we study diameters of the pair digraphs of permutation automata and construct n-state permutation automata with diameter (formula presented). © Springer International Publishing AG 2017

Development and preliminary evaluation of the VPS ReplaySuite: a virtual double-headed microscope for pathology

BACKGROUND: Advances in computing and telecommunications have resulted in the availability of a range of online tools for use in pathology training and quality assurance. The majority focus on either enabling pathologists to examine and diagnose cases, or providing image archives that serve as reference material. Limited emphasis has been placed on analysing the diagnostic process used by pathologists to reach a diagnosis and using this as a resource for improving diagnostic performance. METHODS: The ReplaySuite is an online pathology software tool that presents archived virtual slide examinations to pathologists in an accessible video-like format, similar to observing examinations with a double-headed microscope. Delivered through a customised web browser, it utilises PHP (Hypertext PreProcessor) to interact with a remote database and retrieve data describing virtual slide examinations, performed using the Virtual Pathology Slide (VPS). To demonstrate the technology and conduct a preliminary evaluation of pathologists opinions on its potential application in pathology training and quality assurance, 70 pathologists were invited to use the application to review their own and other pathologists examinations of 10 needle-core breast biopsies and complete an electronic survey. 9 pathologists participated, and all subsequently completed an exit survey. RESULTS: Of those who replayed an examination by another pathologist, 83.3% (5/6) agreed that replays provided an insight into the examining pathologists diagnosis and 33.3% (2/6) reconsidered their own diagnosis for at least one case. Of those who reconsidered their original diagnosis, all re-classified either concordant with group consensus or original glass slide diagnosis. 77.7% (7/9) of all participants, and all 3 participants who replayed more than 10 examinations stated the ReplaySuite to be of some or great benefit in pathology training and quality assurance. CONCLUSION: Participants conclude the ReplaySuite to be of some or of great potential benefit to pathology training and quality assurance and consider the ReplaySuite to be beneficial in evaluating the diagnostic trace of an examination. The ReplaySuite removes temporal and spatial issues that surround the use of double-headed microscopes by allowing examinations to be reviewed at different times and in different locations to the original examination. While the evaluation set was limited and potentially subject to bias, the response of participants was favourable. Further work is planned to determine whether use of the ReplaySuite can result in improved diagnostic ability

The Bin Area Method: A Computationally Efficient Technique for Analysis of Ventricular and Atrial Intracardiac Electrograms

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74901/1/j.1540-8159.1990.tb02028.x.pd

Intraventricular Electrogram Analysis for Ventricular Tachycardia Detection: Statistical Validation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72298/1/j.1540-8159.1990.tb06860.x.pd

A combined analysis technique for the search for fast magnetic monopoles with the MACRO detector

We describe a search method for fast moving ($\beta > 5 \times 10^{-3}$) magnetic monopoles using simultaneously the scintillator, streamer tube and track-etch subdetectors of the MACRO apparatus. The first two subdetectors are used primarily for the identification of candidates while the track-etch one is used as the final tool for their rejection or confirmation. Using this technique, a first sample of more than two years of data has been analyzed without any evidence of a magnetic monopole. We set a 90% CL upper limit to the local monopole flux of $1.5 \times 10^{-15} cm^{-2} s^{-1} sr^{-1}$ in the velocity range $5 \times 10^{-3} \le \beta \le 0.99$ and for nucleon decay catalysis cross section smaller than $\sim 1 mb$.Comment: 29 pages (12 figures). Accepted by Astroparticle Physic

Final results of magnetic monopole searches with the MACRO experiment

We present the final results obtained by the MACRO experiment in the search for GUT magnetic monopoles in the penetrating cosmic radiation, for the range $4\times 10^{-5}< \beta < 1$. Several searches with all the MACRO sub-detectors (i.e. scintillation counters, limited streamer tubes and nuclear track detectors) were performed, both in stand alone and combined ways. No candidates were detected and a 90% Confidence Level (C.L.) upper limit to the local magnetic monopole flux was set at the level of $1.4\times 10^{-16}$ cm$^{-2}$ s$^{-1}$ sr$^{-1}$. This result is the first experimental limit obtained in direct searches which is well below the Parker bound in the whole $\beta$ range in which GUT magnetic monopoles are expected.Comment: 12 pages, Latex, 9 figures and 2 Table