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 $\Sigma_{2k-5}$

Perceptions of Multicultural Training in Predoctoral Internship Programs: A Survey of Interns and Training Directors

Multicultural training at internship sites is a critical component in the preparation of doctoral-level psychologists, so the quality of this training is of the utmost importance. In the following study, the authors examine multicultural training from the perspective of predoctoral interns and training directors at counseling center sites that offer a major or minor rotation in multicultural therapy. Results suggest that perspectives vary between interns and training directors and that there is a great difference in the type of criteria used by each site as evidence of a major or minor rotation. The need for more standardized criteria to define major and minor rotations and suggestions for the Association of Psychology Postdoctoral and Internship Centers, internship training directors, and prospective interns are discussed

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

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

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Transversality of Electromagnetic Waves in the Calculus-Based Introductory Physics Course

Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments are at a level appropriate for students of courses based on such books, and could be readily used by instructors of such courses. Here, we discuss two physical arguments (based on polarization experiments and on lack of monopole electromagnetic radiation), and the full argument for the transversality of (plane) electromagnetic waves based on the integral Maxwell equations. We also show, at a level appropriate for the introductory course, why the electric and magnetic fields in a wave are in phase and the relation of their magnitudes.Comment: 10 pages, 6 figure

Can management intensity be more important than environmental factors? A case study along an extreme elevation gradient from central Italian cereal fields

This paper aims to assess the importance of environmental and management factors determining the weed species composition along a strong elevation gradient. A total of 76 cereal fields (39 low input and 37 intensively managed) were sampled along an elevation gradient in central Italy. Explanatory variables were recorded for each field to elucidate the role of large-scale spatial trends, of site-specific abiotic environmental conditions and of field management characters. Redundancy analysis was used to assess the relative importance of each environmental variable in explaining the variation in species composition. Our results indicate that variation in weed species composition is strongly determined by altitude, mean annual precipitation, mean annual temperature and also by soil characteristics. However, the level of intensification proved to be the most influential variable. There was a significant difference in species richness and composition between low-input and intensively managed fields. Intensification leads to considerable species loss at both lower and higher elevations. Low-input fields had 296 species in total, while intensively managed fields had only 196

A photonic basis for deriving nonlinear optical response

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as coefficients in a power series - nonlinear optical susceptibilities signifying a propensity to generate optical harmonics, for example. Taking the subject to a deeper level requires a more detailed knowledge of the structure and properties of each nonlinear susceptibility tensor, the latter differing in form according to the process under investigation. Typically, the derivations involve intricate development based on time-dependent perturbation theory, assisted by recourse to a set of Feynman diagrams. This paper presents a more direct route to the required results, based on photonic rather than semiclassical principles, and offers a significantly clearer perspective on the photophysics underlying nonlinear optical response. The method, here illustrated by specific application to harmonic generation and down-conversion processes, is simple, intuitive and readily amenable for processes of arbitrary photonic order. © 2009 IOP Publishing Ltd