On the domain wall partition functions of level-1 affine so(n) vertex models

We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil

Cascades: A view from Audience

Cascades on online networks have been a popular subject of study in the past decade, and there is a considerable literature on phenomena such as diffusion mechanisms, virality, cascade prediction, and peer network effects. However, a basic question has received comparatively little attention: how desirable are cascades on a social media platform from the point of view of users? While versions of this question have been considered from the perspective of the producers of cascades, any answer to this question must also take into account the effect of cascades on their audience. In this work, we seek to fill this gap by providing a consumer perspective of cascade. Users on online networks play the dual role of producers and consumers. First, we perform an empirical study of the interaction of Twitter users with retweet cascades. We measure how often users observe retweets in their home timeline, and observe a phenomenon that we term the "Impressions Paradox": the share of impressions for cascades of size k decays much slower than frequency of cascades of size k. Thus, the audience for cascades can be quite large even for rare large cascades. We also measure audience engagement with retweet cascades in comparison to non-retweeted content. Our results show that cascades often rival or exceed organic content in engagement received per impression. This result is perhaps surprising in that consumers didn't opt in to see tweets from these authors. Furthermore, although cascading content is widely popular, one would expect it to eventually reach parts of the audience that may not be interested in the content. Motivated by our findings, we posit a theoretical model that focuses on the effect of cascades on the audience. Our results on this model highlight the balance between retweeting as a high-quality content selection mechanism and the role of network users in filtering irrelevant content

The Causal Structure of Emotions in Aristotle: Hylomorphism, Causal Interaction between Mind and Body, and Intentionality

Recently, a strong hylomorphic reading of Aristotelian emotions has been put forward, one that allegedly eliminates the problem of causal interaction between soul and body. Taking the presentation of emotions in de An. I 1 as a starting point and basic thread, but relying also on the discussion of Rh. II, I will argue that this reading only takes into account two of the four causes of emotions, and that, if all four of them are included into the picture, then a causal interaction of mind and body remains within Aristotelian emotions, independent of how strongly their hylomorphism is understood. Beyond the discussion with this recent reading, the analysis proposed of the fourfold causal structure of emotions is also intended as a hermeneutical starting point for a comprehensive analysis of particular emotions in Aristotle. Through the different causes Aristotle seems to account for many aspects of the complex phenomenon of emotion, including its physiological causes, its mental causes, and its intentional object

Critical Velocity of Vortex Nucleation in Rotating Superfluid 3He-A

We have measured the critical velocity v_c at which 3He-A in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that v_c is distributed between a maximum and minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentum l(r) in the cylinder. Slow cool down through T_c in rotation yields l(r) textures for which the measured v_c's are in good agreement with the calculated instability of the expected l texture.Comment: 4 pages, 3 figure

A Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron

Recoil proton polarization observables were measured for both the p($\vec {\rm e}$,e$^\prime\vec{\rm p}\,$) and d($\vec {\rm e}$,e$^\prime\vec{\rm p}\,)$n reactions at two values of Q$^2$ using a newly commissioned proton Focal Plane Polarimeter at the M.I.T.-Bates Linear Accelerator Center. The hydrogen and deuterium spin-dependent observables $D_{\ell\ell}$ and $D_{{\ell}t}$, the induced polarization $P_n$ and the form factor ratio $G^p_E/G^p_M$ were measured under identical kinematics. The deuterium and hydrogen results are in good agreement with each other and with the plane-wave impulse approximation (PWIA).Comment: 9 pages, 1 figure; accepted by Phys. Rev. Let

Game saturation of intersecting families

We consider the following combinatorial game: two players, Fast and Slow, claim $k$-element subsets of $[n]=\{1,2,...,n\}$ alternately, one at each turn, such that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed $k$-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone the game's end as long as possible. The game saturation number is the score of the game when both players play according to an optimal strategy. To be precise we have to distinguish two cases depending on which player takes the first move. Let $gsat_F(\mathbb{I}_{n,k})$ and $gsat_S(\mathbb{I}_{n,k})$ denote the score of the saturation game when both players play according to an optimal strategy and the game starts with Fast's or Slow's move, respectively. We prove that $\Omega_k(n^{k/3-5}) \le gsat_F(\mathbb{I}_{n,k}),gsat_S(\mathbb{I}_{n,k}) \le O_k(n^{k-\sqrt{k}/2})$ holds

Theory of High-Tc Superconductivity: Accurate Predictions of Tc

The superconducting transition temperatures of high-Tc compounds based on copper, iron, ruthenium and certain organic molecules are discovered to be dependent on bond lengths, ionic valences, and Coulomb coupling between electronic bands in adjacent, spatially separated layers [1]. Optimal transition temperature, denoted as T_c0, is given by the universal expression $k_BT_c0 = e^2 \Lambda / \ell\zeta$; $\ell$ is the spacing between interacting charges within the layers, \zeta is the distance between interacting layers and \Lambda is a universal constant, equal to about twice the reduced electron Compton wavelength (suggesting that Compton scattering plays a role in pairing). Non-optimum compounds in which sample degradation is evident typically exhibit Tc < T_c0. For the 31+ optimum compounds tested, the theoretical and experimental T_c0 agree statistically to within +/- 1.4 K. The elemental high Tc building block comprises two adjacent and spatially separated charge layers; the factor e^2/\zeta arises from Coulomb forces between them. The theoretical charge structure representing a room-temperature superconductor is also presented.Comment: 7 pages 5 references, 6 figures 1 tabl

Latent Space Model for Multi-Modal Social Data

With the emergence of social networking services, researchers enjoy the increasing availability of large-scale heterogenous datasets capturing online user interactions and behaviors. Traditional analysis of techno-social systems data has focused mainly on describing either the dynamics of social interactions, or the attributes and behaviors of the users. However, overwhelming empirical evidence suggests that the two dimensions affect one another, and therefore they should be jointly modeled and analyzed in a multi-modal framework. The benefits of such an approach include the ability to build better predictive models, leveraging social network information as well as user behavioral signals. To this purpose, here we propose the Constrained Latent Space Model (CLSM), a generalized framework that combines Mixed Membership Stochastic Blockmodels (MMSB) and Latent Dirichlet Allocation (LDA) incorporating a constraint that forces the latent space to concurrently describe the multiple data modalities. We derive an efficient inference algorithm based on Variational Expectation Maximization that has a computational cost linear in the size of the network, thus making it feasible to analyze massive social datasets. We validate the proposed framework on two problems: prediction of social interactions from user attributes and behaviors, and behavior prediction exploiting network information. We perform experiments with a variety of multi-modal social systems, spanning location-based social networks (Gowalla), social media services (Instagram, Orkut), e-commerce and review sites (Amazon, Ciao), and finally citation networks (Cora). The results indicate significant improvement in prediction accuracy over state of the art methods, and demonstrate the flexibility of the proposed approach for addressing a variety of different learning problems commonly occurring with multi-modal social data.Comment: 12 pages, 7 figures, 2 table

Measurement of the Proton's Neutral Weak Magnetic Form Factor

We report the first measurement of the parity-violating asymmetry in elastic electron scattering from the proton. The asymmetry depends on the neutral weak magnetic form factor of the proton which contains new information on the contribution of strange quark-antiquark pairs to the magnetic moment of the proton. We obtain the value $G_M^Z= 0.34 \pm 0.09 \pm 0.04 \pm 0.05$ n.m. at $Q^2=0.1$ (GeV/c)${}^2$.Comment: 4 pages TEX, text available at http://www.krl.caltech.edu/preprints/OAP.htm