Busy Beaver Scores and Alphabet Size

We investigate the Busy Beaver Game introduced by Rado (1962) generalized to non-binary alphabets. Harland (2016) conjectured that activity (number of steps) and productivity (number of non-blank symbols) of candidate machines grow as the alphabet size increases. We prove this conjecture for any alphabet size under the condition that the number of states is sufficiently large. For the measure activity we show that increasing the alphabet size from two to three allows an increase. By a classical construction it is even possible to obtain a two-state machine increasing activity and productivity of any machine if we allow an alphabet size depending on the number of states of the original machine. We also show that an increase of the alphabet by a factor of three admits an increase of activity

Pricing of American call options using regression and numerical integration

Consider the American basket call option in the case where there are N underlying assets, the number of possible exercise times prior to maturity is finite, and the vector of N asset prices is modeled using a Levy process. A numerical method based on regression and numerical integration is proposed to estimate the price of the American option. In the proposed method, we first express the asset prices as nonlinear functions of N uncorrelated standard normal random variables. For a given set of time-t asset prices, we next determine the time-t continuation value by performing a numerical integration along the radial direction in the N-dimensional polar coordinate system for the N uncorrelated standard normal random variables, expressing the integrated value via a regression procedure as a function of the polar angles, and performing a numerical integration over the polar angles. The larger value of the continuation value and the time-t immediate exercise value will then be the option value. The time-t option values over the N-dimensional space may be represented by a quadratic function of the radial distance, with the coefficients of the quadratic function given by second degree polynomials in N-1 polar angles. Partitioning the maturity time T into k* intervals of length Δt, we obtain the time-(k-1)Δt option value from the time-kΔt option values for k= k*, k*-1,…, 1. The time-0 option value is then the price of the American option. It is found that the numerical results for the American option prices based on regression and numerical integration agree well with the simulation results, and exhibit a variation of the prices as we vary the non-normality of the underlying distributions of the assets. To assess the accuracy of the computed price we may use estimated standard error of the computed American option price. The standard error will help us gauge whether the number of selected points along the radial direction and the number of selected polar angles are large enough to achieve the required level of accuracy for the computed American option price

Versatile multiplexed super-resolution imaging of nanostructures by Quencher-Exchange-PAINT

This is the final version of the article. Available from Springer Verlag via the DOI in this record.The optical super-resolution technique DNA-PAINT (Point Accumulation Imaging in Nanoscale Topography) provides a flexible way to achieve imaging of nanoscale structures at ∼10-nanometer resolution. In DNA-PAINT, fluorescently labeled DNA “imager” strands bind transiently and with high specificity to complementary target “docking” strands anchored to the structure of interest. The localization of single binding events enables the assembly of a super-resolution image, and this approach effectively circumvents photobleaching. The solution exchange of imager strands is the basis of Exchange-PAINT, which enables multiplexed imaging that avoids chromatic aberrations. Fluid exchange during imaging typically requires specialized chambers or washes, which can disturb the sample. Additionally, diffusional washout of imager strands is slow in thick samples such as biological tissue slices. Here, we introduce Quencher-Exchange-PAINT—a new approach to Exchange-PAINT in regular open-top imaging chambers—which overcomes the comparatively slow imager strand switching via diffusional imager washout. Quencher-Exchange-PAINT uses “quencher” strands, i.e., oligonucleotides that prevent the imager from binding to the targets, to rapidly reduce unwanted single-stranded imager concentrations to negligible levels, decoupled from the absolute imager concentration. The quencher strands contain an effective dye quencher that reduces the fluorescence of quenched imager strands to negligible levels. We characterized Quencher-Exchange-PAINT when applied to synthetic, cellular, and thick tissue samples. Quencher-Exchange-PAINT opens the way for efficient multiplexed imaging of complex nanostructures, e.g., in thick tissues, without the need for washing steps. [Figure not available: see fulltext.]The work was supported by funding from the Human Frontier Science Program (No. 0027/2013) and the Engineering and Physical Sciences Research Council of the UK (No. EP/N008235/1)

Mesoscale magnetism at the grain boundaries in colossal magnetoresistive films

We report the discovery of mesoscale regions with distinctive magnetic properties in epitaxial La$_{1-x}$Sr$_{x}$MnO$_{3}$ films which exhibit tunneling-like magnetoresistance across grain boundaries. By using temperature-dependent magnetic force microscopy we observe that the mesoscale regions are formed near the grain boundaries and have a different Curie temperature (up to 20 K {\it higher}) than the grain interiors. Our images provide direct evidence for previous speculations that the grain boundaries in thin films are not magnetically and electronically sharp interfaces. The size of the mesoscale regions varies with temperature and nature of the underlying defect.Comment: 4 pages of text, 4 figure

Skyrmion fluctuations at a first-order phase transition boundary

Magnetic skyrmions are topologically protected spin textures with promising prospects for applications in data storage. They can form a lattice state due to competing magnetic interactions and are commonly found in a small region of the temperature - magnetic field phase diagram. Recent work has demonstrated that these magnetic quasi-particles fluctuate at the μeV energy scale. Here, we use a coherent x-ray correlation method at an x-ray free-electron laser to investigate these fluctuations in a magnetic phase coexistence region near a first-order transition boundary where fluctuations are not expected to play a major role. Surprisingly, we find that the relaxation of the intermediate scattering function at this transition differs significantly compared to that deep in the skyrmion lattice phase. The observation of a compressed exponential behavior suggests solid-like dynamics, often associated with jamming. We assign this behavior to disorder and the phase coexistence observed in a narrow field-window near the transition, which can cause fluctuations that lead to glassy behavior

Psychometric evaluation of the Persian Internet Disorder Scale among adolescents

Background and aims: Given the growing epidemiological research interest concerning Internet addiction, brief instruments with a robust theoretical basis are warranted. The Internet Disorder Scale (IDS-15) is one such instrument that can be used to quickly assess the Internet addiction in an individual. However, only two language versions of the IDS-15 have been developed. This study translated the IDS-15 into Persian and examined its psychometric properties using comprehensive psychometric testing. Methods: After ensuring the linguistic validity of the Persian IDS-15, 1,272 adolescents (mean age = 15.53 years; 728 males) completed the IDS-15, Depression Anxiety Stress Scale (DASS), Internet Gaming Disorder Scale – Short Form (IGDS9-SF), and the Bergen Social Media Addiction Scale (BSMAS). Confirmatory factor analysis (CFA), Rasch models, regression analysis, and latent profile analysis (LPA) were carried out to test the psychometric properties of the Persian IDS-15. Results: Both CFA and Rasch supported the construct validity of the Persian IDS-15. Multigroup analysis in CFA and differential item functioning in Rasch indicated that male and female adolescents interpreted the IDS-15 items similarly. Regression analysis showed that the IDS-15 correlated with IGDS9-SF and BSMAS (ΔR2 = .12 and .36, respectively) is stronger than the DASS (ΔR2 = .03–.05). LPA based on IDS-15 suggests three subgroups for the sample. Significant differences in depression, anxiety, IGDS9-SF, and BSMAS were found among the three LPA subgroups. Conclusion: The Persian IDS-15 has robust psychometric properties as evidenced by both classical test theory and Rasch analysis

An invisibility cloak using silver nanowires

In this paper, we use the parameter retrieval method together with an analytical effective medium approach to design a well-performed invisible cloak, which is based on an empirical revised version of the reduced cloak. The designed cloak can be implemented by silver nanowires with elliptical cross-sections embedded in a polymethyl methacrylate host. This cloak is numerically proved to be robust for both the inner hidden object as well as incoming detecting waves, and is much simpler thus easier to manufacture when compared with the earlier proposed one [Nat. Photon. 1, 224 (2007)].Comment: 7 pages, 4 figures, 2 table

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators [1, 2]. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in the periodic potential of interfering laser beams, a method which so far has only been applied to explore simple lattice structures [3, 4]. Here we report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other - a situation which has recently attracted considerable theoretical interest [5-9], but seems extremely challenging to observe in solids [10]. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide an avenue to explore many-body phases resulting from the interplay of complex lattice geometries with interactions [11, 12]

Are genetic risk factors for psychosis also associated with dimension-specific psychotic experiences in adolescence?

Psychosis has been hypothesised to be a continuously distributed quantitative phenotype and disorders such as schizophrenia and bipolar disorder represent its extreme manifestations. Evidence suggests that common genetic variants play an important role in liability to both schizophrenia and bipolar disorder. Here we tested the hypothesis that these common variants would also influence psychotic experiences measured dimensionally in adolescents in the general population. Our aim was to test whether schizophrenia and bipolar disorder polygenic risk scores (PRS), as well as specific single nucleotide polymorphisms (SNPs) previously identified as risk variants for schizophrenia, were associated with adolescent dimension-specific psychotic experiences. Self-reported Paranoia, Hallucinations, Cognitive Disorganisation, Grandiosity, Anhedonia, and Parent-rated Negative Symptoms, as measured by the Specific Psychotic Experiences Questionnaire (SPEQ), were assessed in a community sample of 2,152 16-year-olds. Polygenic risk scores were calculated using estimates of the log of odds ratios from the Psychiatric Genomics Consortium GWAS stage-1 mega-analysis of schizophrenia and bipolar disorder. The polygenic risk analyses yielded no significant associations between schizophrenia and bipolar disorder PRS and the SPEQ measures. The analyses on the 28 individual SNPs previously associated with schizophrenia found that two SNPs in TCF4 returned a significant association with the SPEQ Paranoia dimension, rs17512836 (p-value=2.57x10-4) and rs9960767 (p-value=6.23x10-4). Replication in an independent sample of 16-year-olds (N=3,427) assessed using the Psychotic-Like Symptoms Questionnaire (PLIKS-Q), a composite measure of multiple positive psychotic experiences, failed to yield significant results. Future research with PRS derived from larger samples, as well as larger adolescent validation samples, would improve the predictive power to test these hypotheses further. The challenges of relating adult clinical diagnostic constructs such as schizophrenia to adolescent psychotic experiences at a genetic level are discussed