Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed. The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements. The method is made invariant domain preserving for the Euler equations using convex limiting and is tested on various benchmarks.

A Prevailing-Decree Verifier intended for Cryptographic Etiquettes

In recent years, a number of cryptographic etiquettes have been mechanically verified using a selection of inductive methods. These attestations typically want central a figure of recursive sets of messages, and need deep intuition into why the etiquette is correct. As a result, these proofs frequently require days to weeks of expert effort. We ensure advanced an involuntary verifier, which seems to overawe these glitches for many cryptographic protocols. The code of behavior text to concept a number of first-order invariant the proof commitments mitigating these invariants, along with any user-specified protocol properties are showed from the invariants with a tenacity theorem proved. The individual litheness in construction these invariants is to guesstimate, for each type of nonce and encryption engendered by the protocol, a formulary arresting conditions compulsory for that nonce encryption to be published.

Deep Attentive Ranking Networks for Learning to Order Sentences

We present an attention-based ranking framework for learning to order sentences given a paragraph. Our framework is built on a bidirectional sentence encoder and a self-attention based transformer network to obtain an input order invariant representation of paragraphs. Moreover, it allows seamless training using a variety of ranking based loss functions, such as pointwise, pairwise, and listwise ranking. We apply our framework on two tasks: Sentence Ordering and Order Discrimination. Our framework outperforms various state-of-the-art methods on these tasks on a variety of evaluation metrics. We also show that it achieves better results when using pairwise and listwise ranking losses, rather than the pointwise ranking loss, which suggests that incorporating relative positions of two or more sentences in the loss function contributes to better learning.

Higher-Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics

The dynamical symmetries of 1+1-dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial de Alfaro-Fubini-Furlan, DFF, term) are investigated. The first-order invariant differential operators induce several invariant algebras and superalgebras. Besides the sl(2)⊕u(1) invariance of the Calogero Conformal Mechanics, an osp2∣2 invariant superalgebra, realized by first-order and second-order differential operators, is obtained. The invariant algebras with an infinite tower of generators are given by the universal enveloping algebra of the deformed Heisenberg algebra, which is shown to be equivalent to a deformed version of the Schrödinger algebra. This vector space also gives rise to a higher-spin (gravity) superalgebra. We furthermore prove that the pure and DFF Matrix Calogero PDEs possess isomorphic dynamical symmetries, being related by a similarity transformation and a redefinition of the time variable.