Stratifying quotient stacks and moduli stacks

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S/H] has a geometric quotient S/H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201

Modeling and Experimental Demonstration of a Hopfield Network Analog-to-Digital Converter with Hybrid CMOS/Memristor Circuits

The purpose of this work was to demonstrate the feasibility of building recurrent artificial neural networks with hybrid complementary metal oxide semiconductor (CMOS)/memristor circuits. To do so, we modeled a Hopfield network implementing an analog-to-digital converter (ADC) with up to 8 bits of precision. Major shortcomings affecting the ADC's precision, such as the non-ideal behavior of CMOS circuitry and the specific limitations of memristors, were investigated and an effective solution was proposed, capitalizing on the in-field programmability of memristors. The theoretical work was validated experimentally by demonstrating the successful operation of a 4-bit ADC circuit implemented with discrete Pt/TiO2−x/Pt memristors and CMOS integrated circuit components.National Science Foundation CCF-1028378Air Force Office of Scientific Research FA9550-12-1-0038Ministerio de Economía y Competitividad TEC2012-37868-C04-0

Acoustically driven storage of light in a quantum well

The strong piezoelectric fields accompanying a surface acoustic wave on a semiconductor quantum well structure are employed to dissociate optically generated excitons and efficiently trap the created electron hole pairs in the moving lateral potential superlattice of the sound wave. The resulting spatial separation of the photogenerated ambipolar charges leads to an increase of the radiative lifetime by orders of magnitude as compared to the unperturbed excitons. External and deliberate screening of the lateral piezoelectric fields triggers radiative recombination after very long storage times at a remote location on the sample.Comment: 4 PostScript figures included, Physical Review Letters, in pres

Casimir Effect as a Test for Thermal Corrections and Hypothetical Long-Range Interactions

We have performed a precise experimental determination of the Casimir pressure between two gold-coated parallel plates by means of a micromachined oscillator. In contrast to all previous experiments on the Casimir effect, where a small relative error (varying from 1% to 15%) was achieved only at the shortest separation, our smallest experimental error ($\sim 0.5$%) is achieved over a wide separation range from 170 nm to 300 nm at 95% confidence. We have formulated a rigorous metrological procedure for the comparison of experiment and theory without resorting to the previously used root-mean-square deviation, which has been criticized in the literature. This enables us to discriminate among different competing theories of the thermal Casimir force, and to resolve a thermodynamic puzzle arising from the application of Lifshitz theory to real metals. Our results lead to a more rigorous approach for obtaining constraints on hypothetical long-range interactions predicted by extra-dimensional physics and other extensions of the Standard Model. In particular, the constraints on non-Newtonian gravity are strengthened by up to a factor of 20 in a wide interaction range at 95% confidence.Comment: 17 pages, 7 figures, Sixth Alexander Friedmann International Seminar on Gravitation and Cosmolog

Internet self-efficacy does not predict student use of Internet-mediated educational technology

Two studies tested the hypothesis that use of learning technologies among undergraduate psychology students was associated with higher Internet self-efficacy (ISE). In Study 1, the ISE scores of 86 students were found not to be associated with either attitudes towards, or measured use of, blogs and wikis as part of an IT skills course. ISE was associated with time spent online, and positive attitudes to wikis were associated with higher use. Study 2 measured 163 students’ ISE scores at the beginning and end of the same course. ISE was again not correlated with attitudes towards, or actual measured use of, learning technologies used in the course. However, ISE was shown to increase during the course. Positive attitudes towards wikis and discussion boards were associated with higher use of each. Overall, ISE scores did not influence measured use of a Virtual Learning Environment (VLE, including blogs, wikis and a discussion board), or attitudes towards those technologies. This implies that while ISE is linked to aspects of online behaviour (time spent online) and can be modified by online activity or training, it does not predict student use of educational Internet technologies

High-density information storage in an absolutely defined aperiodic sequence of monodisperse copolyester

Synthesis of a polymer composed of a large discrete number of chemically distinct monomers in an absolutely defined aperiodic sequence remains a challenge in polymer chemistry. The synthesis has largely been limited to oligomers having a limited number of repeating units due to the difficulties associated with the step-by-step addition of individual monomers to achieve high molecular weights. Here we report the copolymers of ??-hydroxy acids, poly(phenyllactic-co-lactic acid) (PcL) built via the cross-convergent method from four dyads of monomers as constituent units. Our proposed method allows scalable synthesis of sequence-defined PcL in a minimal number of coupling steps from reagents in stoichiometric amounts. Digital information can be stored in an aperiodic sequence of PcL, which can be fully retrieved as binary code by mass spectrometry sequencing. The information storage density (bit/Da) of PcL is 50% higher than DNA, and the storage capacity of PcL can also be increased by adjusting the molecular weight (~38???kDa)

Sub-millimeter Tests of the Gravitational Inverse-square Law

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R <= 160 microns, and on two equal-sized large extra dimensions of R <= 130 microns. Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of pseudoscalars with m <= 10 meV/c^2.Comment: 34 pages, 38 figure