Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$

Refractive index of a transparent liquid measured with a concave mirror

This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids. We derived the refractive index equation using Snell's law and the small-angle approximation. We also verified the validity of this method using the traditional spherical mirror and thin-lens Gaussian equations.Comment: IOPart, 8 pages, 4 figure

The RNA recognition motif protein RBM11 is a novel tissue-specific splicing regulator.

Mammalian tissues display a remarkable complexity of splicing patterns. Nevertheless, only few examples of tissue-specific splicing regulators are known. Herein, we characterize a novel splicing regulator named RBM11, which contains an RNA Recognition Motif (RRM) at the amino terminus and a region lacking known homology at the carboxyl terminus. RBM11 is selectively expressed in brain, cerebellum and testis, and to a lower extent in kidney. RBM11 mRNA levels fluctuate in a developmentally regulated manner, peaking perinatally in brain and cerebellum, and at puberty in testis, in concomitance with differentiation events occurring in neurons and germ cells. Deletion analysis indicated that the RRM of RBM11 is required for RNA binding, whereas the carboxyl terminal region permits nuclear localization and homodimerization. RBM11 is localized in the nucleoplasm and enriched in SRSF2-containing splicing speckles. Transcription inhibition/release experiments and exposure of cells to stress revealed a dynamic movement of RBM11 between nucleoplasm and speckles, suggesting that its localization is affected by the transcriptional status of the cell. Splicing assays revealed a role for RBM11 in the modulation of alternative splicing. In particular, RBM11 affected the choice of alternative 5' splice sites in BCL-X by binding to specific sequences in exon 2 and antagonizing the SR protein SRSF1. Thus, our findings identify RBM11 as a novel tissue-specific splicing factor with potential implication in the regulation of alternative splicing during neuron and germ cell differentiation

Radiographic findings in hereditary multiple exostoses and a new theory of the pathogenesis of exostoses.

Analysis of 330 exostoses in 18 patients affected by hereditary multiple exostoses disease suggested a new classification of exostoses as eccentric or full-thickness. Radiographically arrest of metaphyseal remodeling with failure of coning and persistence of the primary metaphyseal trabeculae was evident in full-thickness exostoses. Similar bone lesions can be obtained experimentally with inhibitors of bone turn-over. A localized, peripheral defect in remodeling over a limited time can give a satisfactory explanation also for the origin of eccentric exostoses. The thesis that this is the basic mechanism of exostosis formation is presented

XEN glaucoma treatment system in the management of refractory glaucomas: a short review on trial data and potential role in clinical practice

The recent development of new devices that are significantly less invasive, collectively termed minimally invasive glaucoma surgery, offers new perspective of intraocular pressure reduction with less risk, short operating times, and rapid recovery. The aim of this work is to provide a panoramic review of the currently published clinical data to assess the potential role of XEN gel stent (Allergan PLC, Irvine, CA, USA) in the management of glaucoma, which is the only filtering minimally invasive glaucoma surgery device that allows the subconjunctival filtration. The ab interno placement of the XEN gel stent offers an alternative for lowering intraocular pressure in refractory glaucoma as a final step, and in patients intolerant to medical therapy as an early surgical approach with minimum conjunctival tissue disruption, restricted flow to avoid hypotony, and long-term safety

The effect of different medium compositions and LAB strains on fermentation Volatile Organic Compounds (VOCs) analysed by Proton Transfer Reaction-Time of Flight-Mass Spectrometry (PTR-ToF-MS)

Lactic acid bacteria (LAB) fermentation is a viable approach for producing plant-based flavour compounds; however, little is understood about the impact of different LAB strains and medium compositions on the production of volatile organic compounds (VOCs). This study investigated the impact of the addition of individual amino acids (AAs) (L-leucine, L-isoleucine, L-phenylalanine, L-glutamic acid, L-aspartic acid, L-threonine, or L-methionine) to a defined medium (DM) on the generation of VOCs (after 0, 7, and 14 days) by one of three LAB strains (Levilactobacillus brevis WLP672 (LB672), Lactiplantibacillus plantarum LP100 (LP100), and Pediococcus pentosaceus PP100 (PP100)), using proton transfer reaction-time of flight-mass spectrometry (PTR-ToF-MS). The concentration of m/z 45.031 (t.i. acetaldehyde) was significantly (p < 0.05) higher after 7 days of fermentation by LP100 in the DM supplemented with threonine compared to all other media fermented by all three strains. The concentrations of m/z 49.012 (t.i. methanethiol) and m/z 95.000 (t.i. dimethyl disulfide) were significantly (p < 0.05) higher after 7 days of fermentation by either LP100, PP100, or LB672 in the DM supplemented with methionine compared to all other media. Information on the role of individual AAs on VOCs generation by different LAB strains will help to guide flavour development from the fermentation of plant-based substrate

Suspension of the fiber mode-cleaner launcher and measurement of the high extinction-ratio (10^{-9}) ellipsometer for the Q & A experiment

The Q & A experiment, first proposed and started in 1994, provides a feasible way of exploring the quantum vacuum through the detection of vacuum birefringence effect generated by QED loop diagram and the detection of the polarization rotation effect generated by photon-interacting (pseudo-)scalar particles. Three main parts of the experiment are: (1) Optics System (including associated Electronic System) based on a suspended 3.5-m high finesse Fabry-Perot cavity, (2) Ellipsometer using ultra-high extinction-ratio polarizer and analyzer, and (3) Magnetic Field Modulation System for generating the birefringence and the polarization rotation effect. In 2002, the Q & A experiment achieved the Phase I sensitivity goal. During Phase II, we set (i) to improve the control system of the cavity mirrors for suppressing the relative motion noise, (ii) to enhance the birefringence signal by setting-up a 60-cm long 2.3 T transverse permanent magnet rotatable to 10 rev/s, (iii) to reduce geometrical noise by inserting a polarization-maintaining optical fiber (PM fiber) as a mode cleaner, and (iv) to use ultra-high extinction-ratio (10^{-9}) polarizer and analyzer for ellipsometry. Here we report on (iii) & (iv); specifically, we present the properties of the PM-fiber mode-cleaner, the transfer function of its suspension system, and the result of our measurement of high extinction-ratio polarizer and analyzer.Comment: 8 pages, 6 figures, presented in the 6th Edoardo Amaldi Conference on Gravitational Waves, Okinawa, Japan, June 2005, and accepted by "Journal of Physics: Conference Series". Modifications from version 2 were made based on the referees' comments on figures. Ref. [31] were update

Performance of SNP markers for parentage analysis in the Italian Alpine brown bear using non-invasive samples

Determination of parentage provides valuable information for the conservation of wild populations, for instance, by allowing the monitoring of breeding success and inbreeding. Between 1999 and 2002, nine brown bears (Ursus arctos) were translocated to augment the remnant population of a few surviving individuals in the Italian Alps, but only part of them reproduced, with a higher inbreeding risk occurrence in the long-time. Currently, in the Alpine population, parentage tests are assessed through the analysis of 15 microsatellite loci (STRs), but the reduction of genetic variability in future generations will need the use of additional informative markers. Single nucleotide polymorphisms (SNPs) have been proven to be useful and reliable in individual identification and family reconstruction; moreover, they can perform well on low-quality samples. In this study, we analysed 51 SNPs to generate a SNP multilocus genotype dataset of 54 Alpine brown bears (Ursus arctos) and compared its performance in parentage analysis with the validated STR dataset. We found that SNPs alone are not sufficient to determine parentage relationships, but the combination of SNPs and STRs provided unambiguous parentage assignments. The combined panel also performed better than STRs when true parents were not present in the dataset and, consequently, showed higher values of assignment probabilities

Differential contribution of the MTOR and MNK pathways to the regulation of mRNA translation in meiotic and postmeiotic mouse male germ cells

Translation of stored mRNAs accounts for protein synthesis during the transcriptionally inactive stages of spermatogenesis. A key step in mRNA translation is the assembly of the initiation complex EIF4F, which is regulated by the MTOR (mammalian target of rapamycin) and MNK1/2 (MAP kinase-interacting kinase 1 and 2) pathways. We investigated the expression and activity of regulatory proteins of these pathways in male germ cells at different stages of differentiation. All translation factors analyzed were expressed in germ cells throughout spermatogenesis. However, while EIF4G and PABP1 (poly[A]-binding protein 1) were more abundant in postmeiotic cells, MTOR and its target EIF4EBP1 (4E-BP1) decreased steadily during spermatogenesis. In vivo labeling showed that pachytene spermatocytes display higher rates of protein synthesis, which are partially dependent on MTOR and MNK activity. By contrast, haploid spermatids are characterized by lower levels of protein synthesis, which are independent of the activity of these pathways. Accordingly, MTOR and MNK activity enhanced formation of the EIF4F complex in pachytene spermatocytes but not in round spermatids. Moreover, external cues differentially modulated the activity of these pathways in meiotic and haploid cells. Heat shock decreased MTOR and MNK activity in pachytene spermatocytes, whereas round spermatids were much less sensitive. On the other hand, treatment with the phosphatase inhibitor okadaic acid activated MTOR and MNK in both cell types. These results indicate that translational regulation is differentially dependent on the MTOR and MNK pathways in mouse spermatocytes and spermatids and suggest that the late stages of germ cell differentiation display constitutive assembly of the translation initiation complex

Q & A Experiment to Search for Vacuum Dichroism, Pseudoscalar-Photon Interaction and Millicharged Fermions

A number of experiments are underway to detect vacuum birefringence and dichroism -- PVLAS, Q & A, and BMV. Recently, PVLAS experiment has observed optical rotation in vacuum by a magnetic field (vacuum dichroism). Theoretical interpretations of this result include a possible pseudoscalar-photon interaction and the existence of millicharged fermions. Here, we report the progress and first results of Q & A (QED [quantum electrodynamics] and Axion) experiment proposed and started in 1994. A 3.5-m high-finesse (around 30,000) Fabry-Perot prototype detector extendable to 7-m has been built and tested. We use X-pendulums and automatic control schemes developed by the gravitational-wave detection community for mirror suspension and cavity control. To polarize the vacuum, we use a 2.3-T dipole permanent magnet, with 27-mm-diameter clear borehole and 0.6-m field length,. In the experiment, the magnet is rotated at 5-10 rev/s to generate time-dependent polarization signal with twice the rotation frequency. Our ellipsometer/polarization-rotation-detection-system is formed by a pair of Glan-Taylor type polarizing prisms with extinction ratio lower than 10-8 together with a polarization modulating Faraday Cell with/without a quarter wave plate. We made an independent calibration of our apparatus by performing a measurement of gaseous Cotton-Mouton effect of nitrogen. We present our first experimental results and give a brief discussion of our experimental limit on pseudo-scalar-photon interaction and millicharged fermions.Comment: 21 pages, 13 figures, submitted to Modern Physics Letter