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

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

Cloning and characterization of mouse UBPy, a deubiquitinating enzyme that interacts with the Ras guanine nucleotide exchange factor CDC25(Mm)/Ras-GRF1

We used yeast "two-hybrid" screening to isolate cDNA-encoding proteins interacting with the N-terminal domain of the Ras nucleotide exchange factor CDC25(Mm). Three independent overlapping clones were isolated from a mouse embryo cDNA library. The full-length cDNA was cloned by RACE-polymerase chain reaction. It encodes a large protein (1080 amino acids) highly homologous to the human deubiquitinating enzyme hUBPy and contains a well conserved domain typical of ubiquitin isopeptidases. Therefore we called this new protein mouse UBPy (mUBPy). Northern blot analysis revealed a 4-kilobase mRNA present in several mouse tissues and highly expressed in testis; a good level of expression was also found in brain, where CDC25(Mm) is exclusively expressed. Using a glutathione S-transferase fusion protein, we demonstrated an "in vitro" interaction between mUBPy and the N-terminal half (amino acids 1-625) of CDC25(Mm). In addition "in vivo" interaction was demonstrated after cotransfection in mammalian cells. We also showed that CDC25Mm, expressed in HEK293 cells, is ubiquitinated and that the coexpression of mUBPy decreases its ubiquitination. In addition the half-life of CDC25Mm protein was considerably increased in the presence of mUBPy. The specific function of the human homolog hUBPy is not defined, although its expression was correlated with cell proliferation. Our results suggest that mUBPy may play a role in controlling degradation of CDC25(Mm), thus regulating the level of this Ras-guanine nucleotide exchange factor

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

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

Minimising Communication in Honest-Majority MPC by Batchwise Multiplication Verification

In this paper, we present two new and very communication-efficient protocols for maliciously secure multi-party computation over fields in the honest-majority setting with abort. Our first protocol improves a recent protocol by Lindell and Nof. Using the so far overlooked tool of batchwise multiplication verification, we speed up their technique for checking correctness of multiplications (with some other improvements), reducing communication by 2x to 7x. In particular, in the 3PC setting, each party sends only two field elements per multiplication. We also show how to achieve fairness, which Lindell and Nof left as an open problem. Our second protocol again applies batchwise multiplication verification, this time to perform 3PC by letting two parties perform the SPDZ protocol using triples generated by a third party and verified batchwise. In this protocol, each party sends only 4/3 field elements during the online phase and 5/3 field elements during the preprocessing phase

DDH-Like Assumptions Based on Extension Rings

Abstract. We introduce and study a new type of DDH-like assumptions based on groups of prime order q. Whereas standard DDH is based on encoding elements of Fq “in the exponent ” of elements in the group, we ask what happens if instead we put in the exponent elements of the extension ring Rf = Fq[X]/(f) where f is a degree-d polynomial. The decision problem that follows naturally reduces to the case where f is irreducible. This variant is called the d-DDH problem, where 1-DDH is standard DDH. We show in the generic group model that d-DDH is harder than DDH for d&gt; 1 and that we obtain, in fact, an infinite hierarchy of progressively weaker assumptions whose complexities lie “between” DDH and CDH. This leads to a large number of new schemes because virtually all known DDH-based constructions can very easily be upgraded to be based on d-DDH. We use the same construction and security proof but get better security and moreover, the amortized complexity (e.g, computation per encrypted bit) is the same as when using DDH. We also show that d-DDH, just like DDH, is easy in bilinear groups. We therefore suggest a different type of assumption, the d-vector DDH problems (d-VDDH), which are based on f(X) = X d, but with a twist to avoid problems with reducible polynomials. We show in the generic group model that d-VDDH is hard in bilinear groups and that the problems become harder with increasing d. We show that hardness of d-VDDH implies CCA-secure encryption, efficient Naor-Reingold style pseudorandom functions, and auxiliary input secure encryption. This can be seen as an alternative to the known family of k-LIN assumptions.

A Closed-Form Solution of Rotation Invariant Spherical Harmonic Features in Diffusion MRI

International audienceRotation invariant features are an indispensable tool for characterizing diffusion Magnetic Resonance Imaging (MRI) and in particular for brain tissue microstructure estimation. In this work, we propose a new mathematical framework for efficiently calculating a complete set of such invariants from any spherical function. Specifically, our method is based on the spherical harmonics series expansion of a given function of any order and can be applied directly to the resulting coefficients by performing a simple integral operation analytically. This enable us to derive a general closed-form equation for the invariants. We test our invariants on the diffusion MRI fiber orientation distribution function obtained from the diffusion signal both in-vivo and in synthetic data. Results show how it is possible to use these invariants for characterizing the white matter using a small but complete set of features