Instantons on General Noncommutative R^4

We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge and found that it is an integer, independent of the noncommutative parameters $\theta_{1,2}$.Comment: 14 pages, LaTeX; deleted some confusing statements in the U(1) 1-instanton case, added ref

Heavy Tails, Generalized Coding, and Optimal Web Layout

This paper considers Web layout design in the spirit of source coding for data compression and rate distortion theory, with the aim of minimizing the average size of files downloaded during Web browsing sessions. The novel aspect here is that the object of design is layout rather than codeword selection, and is subject to navigability constraints. This produces statistics for file transfers that are heavy tailed, completely unlike standard Shannon theory, and provides a natural and plausible explanation for the origin of observed power laws in Web traffic. We introduce a series of theoretical and simulation models for optimal Web layout design with varying levels of analytic tractability and realism with respect to modeling of structure, hyperlinks, and user behavior. All models produce power laws which are striking both for their consistency with each other and with observed data, and their robustness to modeling assumptions. These results suggest that heavy tails are a permanent and ubiquitous feature of Internet traffic, and not an artifice of current applications or user behavior. They also suggest new ways of thinking about protocol design that combines insights from information and control theory with traditional networking

Topological Charge of Noncommutative ADHM Instanton

We analytically calculate the topological charge of the noncommutative ADHM U(N) k-instanton using the Corrigan's identity and find that the result is exactly the instanton number k.Comment: 13 pages, LaTeX; typos correcte

ATM: Action Temporality Modeling for Video Question Answering

Despite significant progress in video question answering (VideoQA), existing methods fall short of questions that require causal/temporal reasoning across frames. This can be attributed to imprecise motion representations. We introduce Action Temporality Modeling (ATM) for temporality reasoning via three-fold uniqueness: (1) rethinking the optical flow and realizing that optical flow is effective in capturing the long horizon temporality reasoning; (2) training the visual-text embedding by contrastive learning in an action-centric manner, leading to better action representations in both vision and text modalities; and (3) preventing the model from answering the question given the shuffled video in the fine-tuning stage, to avoid spurious correlation between appearance and motion and hence ensure faithful temporality reasoning. In the experiments, we show that ATM outperforms previous approaches in terms of the accuracy on multiple VideoQAs and exhibits better true temporality reasoning ability

Computational Design of Flexible Electride with Nontrivial Band Topology

Electrides, with their excess electrons distributed in crystal cavities playing the role of anions, exhibit a variety of unique electronic and magnetic properties. In this work, we employ the first-principles crystal structure prediction to identify a new prototype of A3B electride in which both interlayer spacings and intralayer vacancies provide channels to accommodate the excess electrons in the crystal. This A3B type of structure is calculated to be thermodynamically stable for two alkaline metals oxides (Rb3O and K3O). Remarkably, the unique feature of multiple types of cavities makes the spatial arrangement of anionic electrons highly flexible via elastic strain engineering and chemical substitution, in contrast to the previously reported electrides characterized by a single topology of interstitial electrons. More importantly, our first-principles calculations reveal that Rb3O is a topological Dirac nodal line semimetal, which is induced by the band inversion at the general electronic k momentums in the Brillouin zone associated with the intersitial electric charges. The discovery of flexible electride in combining with topological electronic properties opens an avenue for electride design and shows great promises in electronic device applications

Compact and high-performance vortex mode sorter for multi-dimensional multiplexed fiber communication systems

With the amplitude, time, wavelength/frequency, phase, and polarization/spin parameter dimensions of the light wave/photon almost fully utilized in both classical and quantum photonic information systems, orbital angular momentum (OAM) carried by optical vortex modes is regarded as a new modal parameter dimension for further boosting the capacity and performance of the systems. To exploit the OAM mode space for such systems, stringent performance requirements on a pair of OAM mode multiplexer and demultiplexer (also known as mode sorters) must be met. In this work, we implement a newly discovered optical spiral transformation to achieve a low-cross-Talk, wide-opticalbandwidth, polarization-insensitive, compact, and robust OAM mode sorter that realizes the desired bidirectional conversion between seven co-Axial OAM modes carried by a ring-core fiber and seven linearly displaced Gaussian-like modes in parallel single-mode fiber channels. We further apply the device to successfully demonstrate high-spectralefficiency and high-capacity data transmission in a 50-km OAM fiber communication link for the first time, in which a multi-dimensional multiplexing scheme multiplexes eight orbital-spin vortex mode channels with each mode channel simultaneously carrying 10 wavelength-division multiplexing channels, demonstrating the promising potential of both the OAM mode sorter and the multi-dimensional multiplexed OAM fiber systems enabled by the device. Our results pave the way for futureOAM-based multi-dimensional communication systems