Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion

We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state, are exactly determined as a series expansion in the cumulants of the multiplicities of the potential and hopping energies assumed by the system during its long-time evolution. Once these cumulants are known, even at a finite order, our approach provides the ground state analytically as a function of the Hamiltonian parameters. A scenario of possible applications of this analyticity property is discussed.Comment: 26 pages, 5 figure

Rigidity percolation on aperiodic lattices

We studied the rigidity percolation (RP) model for aperiodic (quasi-crystal) lattices. The RP thresholds (for bond dilution) were obtained for several aperiodic lattices via computer simulation using the "pebble game" algorithm. It was found that the (two rhombi) Penrose lattice is always floppy in view of the RP model. The same was found for the Ammann's octagonal tiling and the Socolar's dodecagonal tiling. In order to impose the percolation transition we used so c. "ferro" modification of these aperiodic tilings. We studied as well the "pinwheel" tiling which has "infinitely-fold" orientational symmetry. The obtained estimates for the modified Penrose, Ammann and Socolar lattices are respectively: $p_{cP} =0.836\pm 0.002$, $p_{cA} = 0.769\pm0.002$, $p_{cS} = 0.938\pm0.001$. The bond RP threshold of the pinwheel tiling was estimated to $p_c = 0.69\pm0.01$. It was found that these results are very close to the Maxwell (the mean-field like) approximation for them.Comment: 9 LaTeX pages, 3 PostScript figures included via epsf.st

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size $3n+1$ are in a bijection with binary trees of size $n$.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Large-scale stochastic flood hazard analysis applied to the Po River

Reliable hazard analysis is crucial in the flood risk management of river basins. For the floodplains of large, developed rivers, flood hazard analysis often needs to account for the complex hydrology of multiple tributaries and the potential failure of dikes. Estimating this hazard using deterministic methods ignores two major aspects of large-scale risk analysis: the spatial–temporal variability of extreme events caused by tributaries, and the uncertainty of dike breach development. Innovative stochastic methods are here developed to account for these uncertainties and are applied to the Po River in Italy. The effects of using these stochastic methods are compared against deterministic equivalents, and the methods are combined to demonstrate applications for an overall stochastic hazard analysis. The results show these uncertainties can impact extreme event water levels by more than 2 m at certain channel locations, and also affect inundation and breaching patterns. The combined hazard analysis allows for probability distributions of flood hazard and dike failure to be developed, which can be used to assess future flood risk management measures

Human neck reflex adaptation towards the frequency content of anterior-posterior torso perturbations

Introduction: Reflex modulation has been extensively reported during posture maintenance in response to task instructions, and to perturbation type, bandwidth and amplitude. For the head-neck system the modulation of the vestibulocollic (VCR) and cervicocollic (CCR) reflexes is essential to maintain upright head posture during unexpected disturbances. Previous studies have estimated that VCR and CCR contribute equally during perturbations in the sagittal plane; however, their modulation with respect to the properties of the disturbance remains unclear. This study seeks to establish how neck reflexes are modulated during perturbations with varying properties and how each reflex contributes to stabilization behavior. We hypothesized that VCR and CCR (a) modulate according to the perturbation bandwidth, (b) are unaffected by the perturbation amplitude and (c) increase when performing a visual acuity task. Methods: Twelve subjects were perturbed via the torso while restrained in a seated position on a motion platform. The anterior-posterior perturbations varied in bandwidth from 0.3 Hz to a maximum frequency of 1.2, 2.0, 4.0 and 8.0 Hz, at three different amplitudes, and with eyes open and closed. Results: Head kinematics and neck muscle EMG demonstrated significant (P < 0.05) changes due to bandwidth, which through modeling and closed loop identification were attributed to modulation of VCR and CCR gains. VCR and CCR demonstrated dominant contributions to stabilization during high (8.0 Hz) and low bandwidth (1.2 and 2.0 Hz) perturbations respectively, and equivalent contributions during mid bandwidth perturbations (4.0 Hz). However both were attenuated when perturbations exceeded the systems natural frequency (~2-3 Hz). Amplitude had an effect only for the lowest amplitude relative to other conditions attributed to thresholding properties of the semicircular canals. With eyes closed reflex gains decreased, attributed to the reduced ability to discriminate self-motion without vision. Conclusions: To maintain head-upright posture adaptations of neck reflexes are observed to occur due to perturbation frequency and visual task conditions but not amplitude. Estimation of reflex contributions demonstrates that previous literature has underestimated the contribution of CCR, particularly during low frequency perturbations

Liposomal clodronate inhibition of osteoclastogenesis and osteoinduction by submicrostructured beta-tricalcium phosphate

Bone graft substitutes such as calcium phosphates are subject to the innate inflammatory reaction, which may bear important consequences for bone regeneration. We speculate that the surface architecture of osteoinductive β-tricalcium phosphate (TCP) stimulates the differentiation of invading monocyte/macrophages into osteoclasts, and that these cells may be essential to ectopic bone formation. To test this, porous TCP cubes with either submicron-scale surface architecture known to induce ectopic bone formation (TCPs, positive control) or micron-scale, non-osteoinductive surface architecture (TCPb, negative control) were subcutaneously implanted on the backs of FVB strain mice for 12 weeks. Additional TCPs samples received local, weekly injections of liposome-encapsulated clodronate (TCPs + LipClod) to deplete invading monocyte/macrophages. TCPs induced osteoclast formation, evident by positive tartrate resistant acid phosphatase (TRAP) cytochemical staining and negative macrophage membrane marker F4/80 immunostaining. No TRAP positive cells were found in TCPb or TCPs + LipClod, only F4/80 positive macrophages and foreign body giant cells. TCPs stimulated subcutaneous bone formation in all implants, while no bone could be found in TCPb or TCPs + LipClod. In agreement, expression of bone and osteoclast gene markers was upregulated in TCPs versus both TCPb and TCPs + LipClod, which were equivalent. In summary, submicron-scale surface structure of TCP induced osteoclastogenesis and ectopic bone formation in a process that is blocked by monocyte/macrophage depletion

Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces

Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formalism is considerably larger than is usually supposed. Applying the powerful consequences of model sets we derive the diffractive nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his 65th birthda

Occurrence and diversity of Xanthomonas campestris pv. campestris in vegetable brassica fields in Nepal

Black rot caused by Xanthomonas campestris pv. campestris was found in 28 sampled cabbage fields in five major cabbage-growing districts in Nepal in 2001 and in four cauliflower fields in two districts and a leaf mustard seed bed in 2003. Pathogenic X. campestris pv. campestris strains were obtained from 39 cabbage plants, 4 cauliflower plants, and 1 leaf mustard plant with typical lesions. Repetitive DNA polymerase chain reaction-based fingerprinting (rep-PCR) using repetitive extragenic palindromic, enterobacterial repetitive intergenic consensus, and BOX primers was used to assess the genetic diversity. Strains were also race typed using a differential series of Brassica spp. Cabbage strains belonged to five races (races 1, 4, 5, 6, and 7), with races 4, 1, and 6 the most common. All cauliflower strains were race 4 and the leaf mustard strain was race 6. A dendrogram derived from the combined rep-PCR profiles showed that the Nepalese X. campestris pv. campestris strains clustered separately from other Xanthomonas spp. and pathovars. Race 1 strains clustered together and strains of races 4, 5, and 6 were each split into at least two clusters. The presence of different races and the genetic variability of the pathogen should be considered when resistant cultivars are bred and introduced into regions in Nepal to control black rot of brassicas

Theory of high harmonic generation in relativistic laser interaction with overdense plasma

High harmonic generation due to the interaction of a short ultra relativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultra relativistic similarity theory we show that the high harmonic spectrum is universal, i.e. it does not depend on the interaction details. The spectrum includes the power law part $I_n\propto n^{-8/3}$ for $n<\sqrt{8\alpha}\gamma_{\max}^3$, followed by exponential decay. Here $\gamma_{\max}$ is the largest relativistic $\gamma$-factor of the plasma surface and $\alpha$ is the second derivative of the surface velocity at this moment. The high harmonic cutoff at $\propto \gamma_{\max}^3$ is parametrically larger than the $4 \gamma_{\max}^2$ predicted by the ``oscillating mirror'' model based on the Doppler effect. The cornerstone of our theory is the new physical phenomenon: spikes in the relativistic $\gamma$-factor of the plasma surface. These spikes define the high harmonic spectrum and lead to attosecond pulses in the reflected radiation.Comment: 12 pages, 9 figure