Liouville theory and uniformization of four-punctured sphere

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.Comment: 17 pages, no figure

State of Alaska Election Security Project Phase 2 Report

A laska’s election system is among the most secure in the country, and it has a number of safeguards other states are now adopting. But the technology Alaska uses to record and count votes could be improved— and the state’s huge size, limited road system, and scattered communities also create special challenges for insuring the integrity of the vote. In this second phase of an ongoing study of Alaska’s election security, we recommend ways of strengthening the system—not only the technology but also the election procedures. The lieutenant governor and the Division of Elections asked the University of Alaska Anchorage to do this evaluation, which began in September 2007.Lieutenant Governor Sean Parnell. State of Alaska Division of Elections.List of Appendices / Glossary / Study Team / Acknowledgments / Introduction / Summary of Recommendations / Part 1 Defense in Depth / Part 2 Fortification of Systems / Part 3 Confidence in Outcomes / Conclusions / Proposed Statement of Work for Phase 3: Implementation / Reference

Naturalistic Affective Expression Classification by a Multi-Stage Approach Based on Hidden Markov Models

In naturalistic behaviour, the affective states of a person change at a rate much slower than the typical rate at which video or audio is recorded (e.g. 25fps for video). Hence, there is a high probability that consecutive recorded instants of expressions represent a same affective content. In this paper, a multi-stage automatic affective expression recognition system is proposed which uses Hidden Markov Models (HMMs) to take into account this temporal relationship and finalize the classification process. The hidden states of the HMMs are associated with the levels of affective dimensions to convert the classification problem into a best path finding problem in HMM. The system was tested on the audio data of the Audio/Visual Emotion Challenge (AVEC) datasets showing performance significantly above that of a one-stage classification system that does not take into account the temporal relationship, as well as above the baseline set provided by this Challenge. Due to the generality of the approach, this system could be applied to other types of affective modalities

Characterization of a dense aperture array for radio astronomy

EMBRACE@Nancay is a prototype instrument consisting of an array of 4608 densely packed antenna elements creating a fully sampled, unblocked aperture. This technology is proposed for the Square Kilometre Array and has the potential of providing an extremely large field of view making it the ideal survey instrument. We describe the system,calibration procedures, and results from the prototype.Comment: 17 pages, accepted for publication in A&

High resolution photoassociation spectroscopy of the excited c3 + 1 potential of 23Na133Cs

We report on photoassociation spectroscopy probing the c 3 Σ + 1 potential of the bialkali NaCs molecule, identifying 11 vibrational lines between v ′ = 0 and v ′ = 25 of the excited c 3 Σ + 1 potential and fitting their rotational and hyperfine structure. The observed lines are assigned by fitting to an effective Hamiltonian model of the excited-state structure with rotational and hyperfine constants as free parameters. We discuss unexpected broadening of select vibrational lines and its possible link to strong spin-orbit coupling of the c 3 Σ + 1 potential with the nearby b 3 Π 1 and B 1 Π 1 manifolds. Finally, we report use of the v ′ = 22 line as an intermediate state for two-photon transfer of weakly bound Feshbach molecules to the rovibrational ground state of the X 1 Σ + manifold.NSF (Grant No. PHY-2110225), the AFOSR (Grant No. FA9550-19-1-0089)Grant No. TC-18-003). J.T.Z. was supported by a National Defense Science and Engineering Graduate Fellowship.Spanish Projects No. PID2020-113390GB-I00 (MICIN), No. PY20-00082 (Junta de Andalucía),A-FQM-52-UGR20 (ERDF–University of Granada) and Andalusian Research Group FQM-20

Snow spectral albedo at Summit, Greenland: measurements and numerical simulations based on physical and chemical properties of the snowpack

The broadband albedo of surface snow is determined both by the near-surface profile of the physical and chemical properties of the snowpack and by the spectral and angular characteristics of the incident solar radiation. Simultaneous measurements of the physical and chemical properties of snow were carried out at Summit Camp, Greenland (72°36´ N, 38°25´ W, 3210 m a.s.l.) in May and June 2011, along with spectral albedo measurements. One of the main objectives of the field campaign was to test our ability to predict snow spectral albedo by comparing the measured albedo to the albedo calculated with a radiative transfer model, using measured snow physical and chemical properties. To achieve this goal, we made daily measurements of the snow spectral albedo in the range 350–2200 nm and recorded snow stratigraphic information down to roughly 80 cm. The snow specific surface area (SSA) was measured using the DUFISSS instrument (DUal Frequency Integrating Sphere for Snow SSA measurement, Gallet et al., 2009). Samples were also collected for chemical analyses including black carbon (BC) and dust, to evaluate the impact of light absorbing particulate matter in snow. This is one of the most comprehensive albedo-related data sets combining chemical analysis, snow physical properties and spectral albedo measurements obtained in a polar environment. The surface albedo was calculated from density, SSA, BC and dust profiles using the DISORT model (DIScrete Ordinate Radiative Transfer, Stamnes et al., 1988) and compared to the measured values. Results indicate that the energy absorbed by the snowpack through the whole spectrum considered can be inferred within 1.10%. This accuracy is only slightly better than that which can be obtained considering pure snow, meaning that the impact of impurities on the snow albedo is small at Summit. In the near infrared, minor deviations in albedo up to 0.014 can be due to the accuracy of radiation and SSA measurements and to the surface roughness, whereas deviations up to 0.05 can be explained by the spatial heterogeneity of the snowpack at small scales, the assumption of spherical snow grains made for DISORT simulations and the vertical resolution of measurements of surface layer physical properties. At 1430 and around 1800 nm the discrepancies are larger and independent of the snow properties; we propose that they are due to errors in the ice refractive index at these wavelengths. This work contributes to the development of physically based albedo schemes in detailed snowpack models, and to the improvement of retrieval algorithms for estimating snow properties from remote sensing data

Distributed Minimum Cut Approximation

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST model). We present a distributed algorithm that, for any weighted graph and any $\epsilon \in (0, 1)$, with high probability finds a cut of size at most $O(\epsilon^{-1}\lambda)$ in $O(D) + \tilde{O}(n^{1/2 + \epsilon})$ rounds, where $\lambda$ is the size of the minimum cut. This algorithm is based on a simple approach for analyzing random edge sampling, which we call the random layering technique. In addition, we also present another distributed algorithm, which is based on a centralized algorithm due to Matula [SODA '93], that with high probability computes a cut of size at most $(2+\epsilon)\lambda$ in $\tilde{O}((D+\sqrt{n})/\epsilon^5)$ rounds for any $\epsilon>0$. The time complexities of both of these algorithms almost match the $\tilde{\Omega}(D + \sqrt{n})$ lower bound of Das Sarma et al. [STOC '11], thus leading to an answer to an open question raised by Elkin [SIGACT-News '04] and Das Sarma et al. [STOC '11]. Furthermore, we also strengthen the lower bound of Das Sarma et al. by extending it to unweighted graphs. We show that the same lower bound also holds for unweighted multigraphs (or equivalently for weighted graphs in which $O(w\log n)$ bits can be transmitted in each round over an edge of weight $w$), even if the diameter is $D=O(\log n)$. For unweighted simple graphs, we show that even for networks of diameter $\tilde{O}(\frac{1}{\lambda}\cdot \sqrt{\frac{n}{\alpha\lambda}})$, finding an $\alpha$-approximate minimum cut in networks of edge connectivity $\lambda$ or computing an $\alpha$-approximation of the edge connectivity requires $\tilde{\Omega}(D + \sqrt{\frac{n}{\alpha\lambda}})$ rounds