Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo Analysis

We extend the model of a 2$d$ solid to include a line of defects. Neighboring atoms on the defect line are connected by ?springs? of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the 3- and 4-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.Comment: 13 figures, 17 page

Potts-Percolation-Gauss Model of a Solid

We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian springs. If the energy is larger than a threshold the "spring" is more likely to fail, while if the energy is lower than the threshold the spring is more likely to be alive. The phase diagram and thermodynamic quantities, such as free energy, numbers of bonds and clusters, and their fluctuations, are determined using renormalization-group and Monte-Carlo techniques.Comment: 10 pages, 12 figure

Testing Linear-Invariant Non-Linear Properties

We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has mostly focused on such tasks for linear properties. The one exception is a test due to Green for "triangle freeness": a function f:\cube^{n}\to\cube satisfies this property if $f(x),f(y),f(x+y)$ do not all equal 1, for any pair x,y\in\cube^{n}. Here we extend this test to a more systematic study of testing for linear-invariant non-linear properties. We consider properties that are described by a single forbidden pattern (and its linear transformations), i.e., a property is given by $k$ points v_{1},...,v_{k}\in\cube^{k} and f:\cube^{n}\to\cube satisfies the property that if for all linear maps L:\cube^{k}\to\cube^{n} it is the case that $f(L(v_{1})),...,f(L(v_{k}))$ do not all equal 1. We show that this property is testable if the underlying matroid specified by $v_{1},...,v_{k}$ is a graphic matroid. This extends Green's result to an infinite class of new properties. Our techniques extend those of Green and in particular we establish a link between the notion of "1-complexity linear systems" of Green and Tao, and graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the proceedings of STACS 200

The O(3P) and N(4S) density measurement at 225 km by ultraviolet absorption and fluorescence in the Apollo-Soyuz test project

The densities of O(3P) and N(4S) at 225 km were determined during the Apollo Soyuz Test Project by a resonance absorption/fluorescence technique in which OI and NI line radiation produced and collimated on board the Apollo was reflected from the Soyuz back to the Apollo for spectral analysis. The two spacecraft maneuvered so that a range of observation angles of plus or minus 15 deg with respect to the normal to the orbital velocity vector was scanned. The measurements were made at night on two consecutive orbits at spacecraft separations of 150 and 500 m. The resulting relative counting rates as function of observation angle were compared to calculated values to determine the oxygen value. This value agrees with mass spectrometric measurements made under similar conditions. The nitrogen value is in good agreement with other measurements and suggests a smaller diurnal variation than is predicted by present models

Ultraviolet absorption: Experiment MA-059

A technique devised to permit the measurement of atmospheric species concentrations is described. This technique involves the application of atomic absorption spectroscopy and the quantitative observation of resonance fluorescence in which atomic or molecular species scatter resonance radiation from a light source into a detector. A beam of atomic oxygen and atomic nitrogen resonance radiation, strong unabsorbable oxygen and nitrogen radiation, and visual radiation was sent from Apollo to Soyuz. The density of atomic oxygen and atomic nitrogen between the two spacecraft was measured by observing the amount of resonance radiation absorbed when the line joining Apollo and Soyuz was perpendicular to their velocity with respect to the ambient atmosphere. Results of postflight analysis of the resonance fluorescence data are discussed

Nasal administration of glutamate decarboxylase (GAD65) peptides induces Th2 responses and prevents murine insulin-dependent diabetes.

We previously demonstrated that a spontaneous Th1 response against glutamate decarboxylase (GAD65) arises in NOD mice at four weeks in age and subsequently T cell autoimmunity spreads both intramolecularly and intermolecularly. Induction of passive tolerance to GAD65, through inactivation of reactive T cells before the onset of autoimmunity, prevented determinant spreading and the development of insulin-dependent diabetes mellitus (IDDM). Here, we examined whether an alternative strategy, designed to induce active tolerance via the engagement of Th2 immune responses to GAD65, before the spontaneous onset of autoimmunity, could inhibit the cascade of Th1 responses that lead to IDDM. We observed that a single intranasal administration of GAD65 peptides to 2-3-wk-old NOD mice induced high levels of IgG1 antibodies to GAD65. GAD65 peptide treated mice displayed greatly reduced IFN gamma responses and increased IL-5 responses to GAD65, confirming the diversion of the spontaneous GAD65 Th1 response toward a Th2 phenotype. Consistent with the induction of an active tolerance mechanism, splenic CD4+ (but not CD8+) T cells from GAD65 peptide-treated mice, inhibited the adoptive transfer of IDDM to NOD-scid/scid mice. This active mechanism not only inhibited the development of proliferative T cell responses to GAD65, it also limited the expansion of autoreactive T cell responses to other beta cell antigens (i.e., determinant spreading). Finally, GAD65 peptide treatment reduced insulitis and long-term IDDM incidence. Collectively, these data suggest that the nasal administration of GAD65 peptides induces a Th2 cell response that inhibits the spontaneous development of autoreactive Th1 responses and the progression of beta cell autoimmunity in NOD mice

Succinct Representation of Codes with Applications to Testing

Motivated by questions in property testing, we search for linear error-correcting codes that have the "single local orbit" property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every "sparse" binary code whose coordinates are indexed by elements of F_{2^n} for prime n, and whose symmetry group includes the group of non-singular affine transformations of F_{2^n} has the single local orbit property. (A code is said to be "sparse" if it contains polynomially many codewords in its block length.) In particular this class includes the dual-BCH codes for whose duals (i.e., for BCH codes) simple bases were not known. Our result gives the first short (O(n)-bit, as opposed to the natural exp(n)-bit) description of a low-weight basis for BCH codes. The interest in the "single local orbit" property comes from the recent result of Kaufman and Sudan (STOC 2008) that shows that the duals of codes that have the single local orbit property under the affine symmetry group are locally testable. When combined with our main result, this shows that all sparse affine-invariant codes over the coordinates F_{2^n} for prime n are locally testable. If, in addition to n being prime, if 2^n-1 is also prime (i.e., 2^n-1 is a Mersenne prime), then we get that every sparse cyclic code also has the single local orbit. In particular this implies that BCH codes of Mersenne prime length are generated by a single low-weight codeword and its cyclic shifts

Achieving sub-diffraction imaging through bound surface states in negative-refracting photonic crystals at the near-infrared

We report the observation of imaging beyond the diffraction limit due to bound surface states in negative refraction photonic crystals. We achieve an effective negative index figure-of-merit [-Re(n)/Im(n)] of at least 380, ~125x improvement over recent efforts in the near-infrared, with a 0.4 THz bandwidth. Supported by numerical and theoretical analyses, the observed near-field resolution is 0.47 lambda, clearly smaller than the diffraction limit of 0.61 lambda. Importantly, we show this sub-diffraction imaging is due to the resonant excitation of surface slab modes, allowing refocusing of non-propagating evanescent waves

Vacillation, indecision and hesitation in moment-by-moment decoding of monkey motor cortex

When choosing actions, we can act decisively, vacillate, or suffer momentary indecision. Studying how individual decisions unfold requires moment-by-moment readouts of brain state. Here we provide such a view from dorsal premotor and primary motor cortex. Two monkeys performed a novel decision task while we recorded from many neurons simultaneously. We found that a decoder trained using 'forced choices' (one target viable) was highly reliable when applied to 'free choices'. However, during free choices internal events formed three categories. Typically, neural activity was consistent with rapid, unwavering choices. Sometimes, though, we observed presumed 'changes of mind': the neural state initially reflected one choice before changing to reflect the final choice. Finally, we observed momentary 'indecision': delay forming any clear motor plan. Further, moments of neural indecision accompanied moments of behavioral indecision. Together, these results reveal the rich and diverse set of internal events long suspected to occur during free choice

SWAS and Arecibo observations of H2O and OH in a diffuse cloud along the line-of-sight to W51

Observations of W51 with the Submillimeter Wave Astronomy Satellite (SWAS) have yielded the first detection of water vapor in a diffuse molecular cloud. The water vapor lies in a foreground cloud that gives rise to an absorption feature at an LSR velocity of 6 km/s. The inferred H2O column density is 2.5E+13 cm-2. Observations with the Arecibo radio telescope of hydroxyl molecules at ten positions in W51 imply an OH column density of 8E+13 cm-2 in the same diffuse cloud. The observed H2O/OH ratio of ~ 0.3 is significantly larger than an upper limit derived previously from ultraviolet observations of the similar diffuse molecular cloud lying in front of HD 154368. The observed variation in H2O/OH likely points to the presence in one or both of these clouds of a warm (T > 400) gas component in which neutral-neutral reactions are important sources of OH and/or H2O.Comment: 15 pages (AASTeX) including 4 (eps) figures. To appear in the Astrophysical Journa