Testing formula satisfaction

We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size

About multiplicities and applications to Bezout numbers

Let $(A,\mathfrak{m},\Bbbk)$ denote a local Noetherian ring and $\mathfrak{q}$ an ideal such that $\ell_A(M/\mathfrak{q}M) < \infty$ for a finitely generated $A$-module $M$. Let \au = a_1,\ldots,a_d denote a system of parameters of $M$ such that $a_i \in \mathfrak{q}^{c_i} \setminus \mathfrak{q}^{c_i+1}$ for $i=1,\ldots,d$. It follows that \chi := e_0(\au;M) - c \cdot e_0(\mathfrak{q};M) \geq 0, where $c = c_1\cdot \ldots \cdot c_d$. The main results of the report are a discussion when $\chi = 0$ resp. to describe the value of $\chi$ in some particular cases. Applications concern results on the multiplicity e_0(\au;M) and applications to Bezout numbers.Comment: 11 pages, to appear Springer INdAM-Series, Vol. 20 (2017

Measuring Beta-Functions with K-Modulation

The precise measurement of the local value of the beta-function at the place of a beam size monitor is necessary for the precise determination of the beam emittance. We developed a new method for the measurement of the beta-function by using of continuous square-wave modulation of the force of the quadrupole and by continuous tune tracking. Measurements were performed at LEP in order to evaluate the precision that can be achieved with this method in the LHC. The paper describes the method and discusses in details the results obtained at LEP for colliding and non-colliding beams

Polaronic signature in the metallic phase of La0.7Ca0.3MnO3 films detected by scanning tunneling spectroscopy

In this work we map tunnel conductance curves with nanometric spatial resolution, tracking polaronic quasiparticle excitations when cooling across the insulator-to-metal transition in La0.7Ca0.3MnO3 films. In the insulating phase the spectral signature of polarons, a depletion of conductance at low bias flanked by peaks, is detected all over the scanned surface. These features are still observed at the transition and persist on cooling into the metallic phase. Polaron-binding energy maps reveal that polarons are not confined to regions embedded in a highly-conducting matrix but are present over the whole field of view both above and below the transition temperature.Comment: 10 pages, 4 figure

Effect of Combined Leaf Extracts of Vernonia amygdalina (Bitter Leaf) and Gongronema latifolium (Utazi) on the Pancreatic beta-Cells of Streptozotocin- Induced Diabetic Rats

The study evaluated the effect of combined extracts of Vernonia amygdalina (VA) and Gongronema latifolium (GL) on the pancreas of streptozotocin (STZ) induced diabetic Wistar rats. Thirty-two (32) albino rats were divided equally into 4 groups. Groups A and B which served as normal (NC) and diabetic (DC) controls respectively, received placebo treatment. The diabetic test groups C and D were respectively treated with combined extracts of VA and GL (200mg/kg b. w., p. o.) and insulin, (humulin 5 IU/kg, s.c.) for 28 days. Thereafter, the animals were sacrificed and blood and pancreas were collected for serum glucose and histological evaluation, respectively. Changes in animal weight were also measured within the period. From the results it was revealed that both the combined extracts and humulin significantly increased the animals’ body weight (p<0.05) from -10.5% reduction in the DC, to 7.6% and 8.9% respectively. In the same order, serum glucose significantly decreased (p<0.05) by 12.49% and 14.96% after the 28-day treatment compared to DC. The extent of reversal of hyperglycemia in the extract treated animals compared well with the insulin treated group. The biochemical results were corroborated with results of histological evaluations: The pancreatic β-cells of DC animals which were distorted and degenerated with shrunken cell mass as against prominent islet cells with normal exocrine pancreas of NC animals became rapidly proliferated upon intervention with the combined extracts, suggesting a possible regeneration of the islet cells. On the otherhand, intervention with humulin did not produce observable differences in the cyto-architecture of the pancreatic islets compared to the diabetic control, confirming an extra-pancreatic mechanism of insulin

Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas

We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a 1+1-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.Comment: 4 pages, 2 figures, RevTex4; as publishe

Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure