K-classes of Brill-Noether loci and a determinantal formula

We prove a determinantal formula for the K-theory class of certain degeneracy loci, and apply it to compute the Euler characteristic of the structure sheaf of the Brill-Noether locus of linear series with special vanishing at marked points. When the Brill-Noether number $\rho$ is zero, we recover the Castelnuovo formula for the number of special linear series on a general curve; when $\rho=1$, we recover the formulas of Eisenbud-Harris, Pirola, and Chan-L\'opez-Pflueger-Teixidor for the arithmetic genus of a Brill-Noether curve of special divisors. Our degeneracy locus formula also specializes to new determinantal expressions for the double Grothendieck polynomials corresponding to 321-avoiding permutations, and gives double versions of the flagged skew Grothendieck polynomials recently introduced by Matsumura. Our result extends the formula of Billey-Jockusch-Stanley expressing Schubert polynomials for 321-avoiding permutations as generating functions for skew tableaux.Comment: 31 pages; v2: stronger Theorem C, and improved expositio

Neural‑Brane: Neural Bayesian Personalized Ranking for Attributed Network Embedding

Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applications, such as node classification, link prediction, and community detection. However, most of the existing methods for network embedding only utilize topological information of a vertex, ignoring a rich set of nodal attributes (such as user profiles of an online social network, or textual contents of a citation network), which is abundant in all real-life networks. A joint network embedding that takes into account both attributional and relational information entails a complete network information and could further enrich the learned vector representations. In this work, we present Neural-Brane, a novel Neural Bayesian Personalized Ranking based Attributed Network Embedding. For a given network, Neural-Brane extracts latent feature representation of its vertices using a designed neural network model that unifies network topological information and nodal attributes. Besides, it utilizes Bayesian personalized ranking objective, which exploits the proximity ordering between a similar node pair and a dissimilar node pair. We evaluate the quality of vertex embedding produced by Neural-Brane by solving the node classification and clustering tasks on four real-world datasets. Experimental results demonstrate the superiority of our proposed method over the state-of-the-art existing methods

NASA/USRA high altitude reconnaissance aircraft

At the equator, the ozone layer ranges from approximately 80,000 to 130,000+ feet which is beyond the capabilities of the ER-2, NASA's current high altitude reconnaissance aircraft. This project is geared to designing an aircraft that can study the ozone layer at the equator. This aircraft must be able to cruise at 130,000 lbs. of payload. In addition, the aircraft must have a minimum of a 6,000 mile range. The low Mach number, payload, and long cruising time are all constraints imposed by the air sampling equipment. A pilot must be able to take control in the event of unforseen difficulties. Three aircraft configurations were determined to be the most suitable for meeting the above requirements, a joined-wing, a bi-plane, and a twin-boom conventional airplane. The techniques used have been deemed reasonable within the limits of 1990 technology. The performance of each configuration is analyzed to investigate the feasibility of the project requirements. In the event that a requirement can not be obtained within the given constraints, recommendations for proposal modifications are given

High-Tc ramp-type Josephson junctions on MgO substrates for Terahertz applications

The authors successfully fabricated high-Tc ramp-type junctions with PrBa2Cu3-xGaxO7-δ (PBCGO: x=0.1, 0.4) barriers on MgO substrates. The junctions showed resistively shunted Josephson junction (RSJ)-like I-V curves with thermally and voltage activated conductivity. The IcRn products for these junctions scaled very well with the Ga-doping. Maximum response of the junctions for 100-GHz millimeter-wave irradiation could be observed up to 12 mV corresponding to 6 THz. Using far infrared laser radiation, we confirmed a terahertz (THz) response of these junctions. These results show promise for THz-wave applications of ramp-type Josephson junctions

Oops! Predicting Unintentional Action in Video

From just a short glance at a video, we can often tell whether a person's action is intentional or not. Can we train a model to recognize this? We introduce a dataset of in-the-wild videos of unintentional action, as well as a suite of tasks for recognizing, localizing, and anticipating its onset. We train a supervised neural network as a baseline and analyze its performance compared to human consistency on the tasks. We also investigate self-supervised representations that leverage natural signals in our dataset, and show the effectiveness of an approach that uses the intrinsic speed of video to perform competitively with highly-supervised pretraining. However, a significant gap between machine and human performance remains. The project website is available at https://oops.cs.columbia.eduComment: 11 pages, 9 figure