Revisit Sparse Polynomial Interpolation based on Randomized Kronecker Substitution

In this paper, a new reduction based interpolation algorithm for black-box multivariate polynomials over finite fields is given. The method is based on two main ingredients. A new Monte Carlo method is given to reduce black-box multivariate polynomial interpolation to black-box univariate polynomial interpolation over any ring. The reduction algorithm leads to multivariate interpolation algorithms with better or the same complexities most cases when combining with various univariate interpolation algorithms. We also propose a modified univariate Ben-or and Tiwarri algorithm over the finite field, which has better total complexity than the Lagrange interpolation algorithm. Combining our reduction method and the modified univariate Ben-or and Tiwarri algorithm, we give a Monte Carlo multivariate interpolation algorithm, which has better total complexity in most cases for sparse interpolation of black-box polynomial over finite fields

The importance of being zero

2018 International Symposium on Symbolic and Algebraic Computation (ISSAC), July 2018, New York, NY, United StatesWe present a deterministic algorithm for deciding if a polynomial ideal, with coefficients in an algebraically closed field K of characteristic zero, of which we know just some very limited data, namely:the number n of variables, and some upper bound for the geometric degree of its zero set in Kn, is or not the zero ideal. The algorithm performs just a finite number of decisions to check whether a point is or not in the zero set of the ideal. Moreover, we extend this technique to test, in the same fashion, if the elimination of some variables in the given ideal yields or not the zero ideal. Finally, the role of this technique in the context of automated theorem proving of elementary geometry statements, is presented, with references to recent documents describing the excellent performance of the already existing prototype version, implemented in GeoGebra.Ministerio de Economía y CompetitividadEuropean Regional Development Fun

Wave breaking turbulence at the offshore front of the Columbia River Plume

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Geophysical Research Letters 41 (2014): 8987–8993, doi:10.1002/2014GL062274.Observations at the Columbia River plume show that wave breaking is an important source of turbulence at the offshore front, which may contribute to plume mixing. The lateral gradient of current associated with the plume front is sufficient to block (and break) shorter waves. The intense whitecapping that then occurs at the front is a significant source of turbulence, which diffuses downward from the surface according to a scaling determined by the wave height and the gradient of wave energy flux. This process is distinct from the shear-driven mixing that occurs at the interface of river water and ocean water. Observations with and without short waves are examined, especially in two cases in which the background conditions (i.e., tidal flows and river discharge) are otherwise identical.This work was supported by the Office of Naval Research, as part of the Data Assimilation and Remote Sensing for Littoral Applications (DARLA) project and in coordination with the Rivers and Inlets (RIVET) program

The inverse moment problem for convex polytopes

The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8

Histologische, funktionelle und spezifische Regeneration nach Durchtrennung der Fila olfactoria beim Goldfisch ( Carassius auratus )

1. Alter dissection of the olfactory libres (fila olfactoria, Fig. 1) in the goldfisch, histological (Fig. 5) as well as functional regeneration takes place. When regeneration of the olfactory fibres was complete, no differences in training and learning behaviour between operated and untreated control animals could be observed (Fig. 2). Specific regeneration could also be proved after dissection of the olfactory fibres: Preoperatively trained discriminative behaviour returned (Figs. 3, 4) when histological regeneration had reached an advanced state (Figs. 6, 7). Higher concentrations of all substances used for odour training were capable of exciting the taste receptors or other struktures outside the olfactory mucosa. The concentrations used for olfactory training, however, were below the thresholds for non-olfactory perception. Neither the surgical procedure nor the anesthesia influenced the memory function. 1. Goldfische können die durchschnittenen Bahnen der Fila olfactoria anatomisch und funktionell regenerieren.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47102/1/359_2004_Article_BF00340911.pd

Effect of acute copper sulfate exposure on olfactory responses to amino acids and pheromones in goldfish (Carassius auratus)

Exposure of olfactory epithelium to environmentally relevant concentrations of copper disrupts olfaction in fish. To examine the dynamics of recovery at both functional and morphological levels after acute copper exposure, unilateral exposure of goldfish olfactory epithelia to 100 μM CuSO4 (10 min) was followed by electro-olfactogram (EOG) recording and scanning electron microscopy. Sensitivity to amino acids (L-arginine and L-serine), generally considered food-related odorants, recovered most rapidly (three days), followed by that to catecholamines(3-O-methoxytyramine),bileacids(taurolithocholic acid) and the steroid pheromone, 17,20 -dihydroxy-4-pregnen- 3-one 20-sulfate, which took 28 days to reach full recovery. Sensitivity to the postovulatory pheromone prostaglandin F2R had not fully recovered even at 28 days. These changes in sensitivity were correlated with changes in the recovery of ciliated and microvillous receptor cell types. Microvillous cells appeared largely unaffected by CuSO4 treatment. Cilia in ciliated receptor neurones, however, appeared damaged one day post-treatment and were virtually absent after three days but had begun to recover after 14 days. Together, these results support the hypothesis that microvillous receptor neurones detect amino acids whereas ciliated receptor neurones were not functional and are responsible for detection of social stimuli (bile acidsandpheromones).Furthermore, differences in sensitivity to copper may be due to different transduction pathways in the different cell types

End-to-end verifiable elections in the standard model

We present the cryptographic implementation of “DEMOS”, a new e-voting system that is end-to-end verifiable in the standard model, i.e., without any additional “setup” assumption or access to a random oracle (RO). Previously known end-to-end verifiable e-voting systems required such additional assumptions (specifically, either the existence of a “randomness beacon” or were only shown secure in the RO model). In order to analyze our scheme, we also provide a modeling of end-to-end verifiability as well as privacy and receipt-freeness that encompasses previous definitions in the form of two concise attack games. Our scheme satisfies end-to-end verifiability information theoretically in the standard model and privacy/receipt-freeness under a computational assumption (subexponential Decisional Diffie Helman). In our construction, we utilize a number of techniques used for the first time in the context of e-voting schemes that include utilizing randomness from bit-fixing sources, zero-knowledge proofs with imperfect verifier randomness and complexity leveraging

Extracellular ATP released by osteoblasts is a key local inhibitor of bone mineralisation

Previous studies have shown that exogenous ATP (>1µM) prevents bone formation in vitro by blocking mineralisation of the collagenous matrix. This effect is thought to be mediated via both P2 receptor-dependent pathways and a receptor-independent mechanism (hydrolysis of ATP to produce the mineralisation inhibitor pyrophosphate, PPi). Osteoblasts are also known to release ATP constitutively. To determine whether this endogenous ATP might exert significant biological effects, bone-forming primary rat osteoblasts were cultured with 0.5-2.5U/ml apyrase (which sequentially hydrolyses ATP to ADP to AMP + 2Pi). Addition of 0.5U/ml apyrase to osteoblast culture medium degraded extracellular ATP to <1% of control levels within 2 minutes; continuous exposure to apyrase maintained this inhibition for up to 14 days. Apyrase treatment for the first 72 hours of culture caused small decreases (≤25%) in osteoblast number, suggesting a role for endogenous ATP in stimulating cell proliferation. Continuous apyrase treatment for 14 days (≥0.5U/ml) increased mineralisation of bone nodules by up to 3-fold. Increases in bone mineralisation were also seen when osteoblasts were cultured with the ATP release inhibitors, NEM and brefeldin A, as well as with P2X1 and P2X7 receptor antagonists. Apyrase decreased alkaline phosphatase (TNAP) activity by up to 60%, whilst increasing the activity of the PPi-generating ecto-nucleotide pyrophosphatase/phosphodiesterases (NPPs) up to 2.7-fold. Both collagen production and adipocyte formation were unaffected. These data suggest that nucleotides released by osteoblasts in bone could act locally, via multiple mechanisms, to limit mineralisation