On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories

Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group $A$, and with vanishing 3-cocycle, is generated by group automorphisms of $A$, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of $A$-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category and braided auto-equivalences of its Drinfeld center. The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and references added. v3: Typos correcte

Correlations between hidden units in multilayer neural networks and replica symmetry breaking

We consider feed-forward neural networks with one hidden layer, tree architecture and a fixed hidden-to-output Boolean function. Focusing on the saturation limit of the storage problem the influence of replica symmetry breaking on the distribution of local fields at the hidden units is investigated. These field distributions determine the probability for finding a specific activation pattern of the hidden units as well as the corresponding correlation coefficients and therefore quantify the division of labor among the hidden units. We find that although modifying the storage capacity and the distribution of local fields markedly replica symmetry breaking has only a minor effect on the correlation coefficients. Detailed numerical results are provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.

Storage capacity of correlated perceptrons

We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A general formalism is introduced using a multi-perceptron costfunction that allows to determine the maximal number of random inputs as a function of the desired values of the correlations. Replica-symmetric results for $K=2$ and $K=3$ are compared with properties of two-layer networks of tree-structure and fixed Boolean function between hidden units and output. The results show which correlations in the hidden layer of multi-layer neural networks are crucial for the value of the storage capacity.Comment: 16 pages, Latex2

Multilayer neural networks with extensively many hidden units

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter the storage capacity if found to scale with the logarithm of the number of implementable Boolean functions. The generalization behaviour is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.Comment: 4 pages, 2 figure

Finite size scaling in neural networks

We demonstrate that the fraction of pattern sets that can be stored in single- and hidden-layer perceptrons exhibits finite size scaling. This feature allows to estimate the critical storage capacity \alpha_c from simulations of relatively small systems. We illustrate this approach by determining \alpha_c, together with the finite size scaling exponent \nu, for storing Gaussian patterns in committee and parity machines with binary couplings and up to K=5 hidden units.Comment: 4 pages, RevTex, 5 figures, uses multicol.sty and psfig.st

Chaos in neural networks with a nonmonotonic transfer function

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and chaos. We examine in detail the structure of the strange attractor and in particular we study the main features of the stable and unstable manifolds, the hyperbolicity of the attractor and the existence of homoclinic intersections. We also discuss the problem of the robustness of the chaos and we prove that in the present model chaotic behaviour is fragile (chaotic regions are densely intercalated with periodicity windows), according to a recently discussed conjecture. Finally we perform an analysis of the microscopic behaviour and in particular we examine the occurrence of damage spreading by studying the time evolution of two almost identical initial configurations. We show that for any choice of the parameters the two initial states remain microscopically distinct.Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E. Originally submitted to the neuro-sys archive which was never publicly announced (was 9905001

Comment on "On the subtleties of searching for dark matter with liquid xenon detectors"

In a recent manuscript (arXiv:1208.5046) Peter Sorensen claims that XENON100's upper limits on spin-independent WIMP-nucleon cross sections for WIMP masses below 10 GeV "may be understated by one order of magnitude or more". Having performed a similar, though more detailed analysis prior to the submission of our new result (arXiv:1207.5988), we do not confirm these findings. We point out the rationale for not considering the described effect in our final analysis and list several potential problems with his study.Comment: 3 pages, no figure

Removing krypton from xenon by cryogenic distillation to the ppq level

The XENON1T experiment aims for the direct detection of dark matter in a cryostat filled with 3.3 tons of liquid xenon. In order to achieve the desired sensitivity, the background induced by radioactive decays inside the detector has to be sufficiently low. One major contributor is the $\beta$-emitter $^{85}$Kr which is an intrinsic contamination of the xenon. For the XENON1T experiment a concentration of natural krypton in xenon $\rm{^{nat}}$Kr/Xe < 200 ppq (parts per quadrillion, 1 ppq = 10$^{-15}$ mol/mol) is required. In this work, the design of a novel cryogenic distillation column using the common McCabe-Thiele approach is described. The system demonstrated a krypton reduction factor of 6.4$\cdot$10$^5$ with thermodynamic stability at process speeds above 3 kg/h. The resulting concentration of $\rm{^{nat}}$Kr/Xe < 26 ppq is the lowest ever achieved, almost one order of magnitude below the requirements for XENON1T and even sufficient for future dark matter experiments using liquid xenon, such as XENONnT and DARWIN

PENERAPAN PENDEKATAN COMPUTATIONAL THINKING UNTUK MENINGKATKAN KEMAMPUAN MENULIS TEKS BERITA PADA KELAS VIII SEKOLAH INDONESIA DAVAO, PHILIPPINES

Dengan menggunakan pendekatan Computational Thinking, penelitian ini memiliki dalam hal peningkatan partisipasi dan kemampuan menulis teks berita peserta didik di kelas VIII Sekolah Indonesia di Davao, Philippines. Studi ini adalah PTK dua siklus. Setiap siklus membahas langkah-langkah PTK, yaitu merencanakan, melaksanakan, mengamati, dan merefleksi. Data pada penelitian ini diproses melalui analisis kuantitatif dan kualitatif. Hasil menunjukkan bahwa partisipasi peserta didik meningkat secara berturut-turut, dengan skor rata-rata 3,0 yang berarti baik dan skor rata-rata 3,5 yang berarti sangat baik. Hasil belajar peserta didik pada siklus I menunjukkan ketuntasan klasik sebesar 77 persen, dengan nilai rata-rata kelas 75. Hasil belajar siklus kedua mencapai ketuntasan 84,6 persen dan nilai rata-rata kelas 80. Data menunjukkan bahwa hasil belajar meningkat setiap siklus. Siklus II juga menunjukkan peningkatan dari target 80 persen menjadi 84,6 persen. Penelitian ini menemukan bahwa peserta didik kelas VIII di Sekolah Indonesia Davao, Filipina, dapat meningkatkan partisipasi dan kemampuan menulis teks berita.This study aims to enhance student learning outcomes in News Text lessons for eighth grade students at the Indonesian School in Davao, Philippines, by implementing a Computational Thinking approach. The study assesses student engagement and their proficiency in writing news texts. It employs a classroom action research methodology conducted over two cycles, each consisting of one session divided into planning, implementation, observation, and reflection stages. Data analysis utilizes both quantitative and qualitative methods. Results indicate a progressive increase in student engagement and learning proficiency across cycles, with average scores improving from 3.0 (good) to 3.5 (very good). Classical completion rates rose from 77% in the first cycle to 84.6% in the second, accompanied by an increase in average scores from 75 to 80. By the end of the second cycle, the study achieved the targeted 80% classical completion rate. Thus, the application of the Computational Thinking approach effectively enhances participation and news text writing abilities among eighth grade students at the Indonesian School in Davao, Philippines

Search for Two-Neutrino Double Electron Capture of 124^{124}Xe with XENON100

Two-neutrino double electron capture is a rare nuclear decay where two electrons are simultaneously captured from the atomic shell. For $^{124}$Xe this process has not yet been observed and its detection would provide a new reference for nuclear matrix element calculations. We have conducted a search for two-neutrino double electron capture from the K-shell of $^{124}$Xe using 7636 kg$\cdot$d of data from the XENON100 dark matter detector. Using a Bayesian analysis we observed no significant excess above background, leading to a lower 90 % credibility limit on the half-life $T_{1/2}>6.5\times10^{20}$ yr. We also evaluated the sensitivity of the XENON1T experiment, which is currently being commissioned, and find a sensitivity of $T_{1/2}>6.1\times10^{22}$ yr after an exposure of 2 t$\cdot$yr.Comment: 6 pages, 4 figure