On the Universality of Linear Recurrences Followed by Nonlinear Projections

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.Comment: Accepted at HLD 2023: 1st Workshop on High-dimensional Learning Dynamic

One-variable fragments of first-order logics

The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases -- notably, the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and intuitionistic logic -- but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in this paper for the one-variable fragment of a semantically-defined first-order logic -- spanning families of intermediate, substructural, many-valued, and modal logics -- to admit a natural axiomatization. More precisely, such an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has the superamalgamation property, building on a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property.Comment: arXiv admin note: text overlap with arXiv:2209.0856

A SA-CASSCF and MS-CASPT2 study on the electronic structure of nitrosobenzene and its relation to its dissociation dynamics.

Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/9875The photodissociation channels of nitrosobenzene (PhNO) induced by a 255 nm photolytic wavelength have been studied with the complete active space self-consistent (CASSCF) method and the multistate second-order multiconfigurational perturbation theory (MS-CASPT2). It is found that there exists a triplet route for photodissociation of the molecule. The reaction mechanism consists on a complex cascade of nonadiabatic electronic transitions involving triple and double conical intersections as well as intersystem crossing. Several of the relevant states (S2, S4, and S5 states) correspond to double excitations. It is worthy to note that the last step of the photodissociation implies an internal conversion process. The experimentally observed velocity pattern of the NO fragment is a signature of such a conical intersection

Thermal Giant Gravitons

We study the giant graviton solution as the AdS_5 X S^5 background is heated up to finite temperature. The analysis employs the thermal brane probe technique based on the blackfold approach. We focus mainly on the thermal giant graviton corresponding to a thermal D3-brane probe wrapped on an S^3 moving on the S^5 of the background at finite temperature. We find several interesting new effects, including that the thermal giant graviton has a minimal possible value for the angular momentum and correspondingly also a minimal possible radius of the S^3. We compute the free energy of the thermal giant graviton in the low temperature regime, which potentially could be compared to that of a thermal state on the gauge theory side. Moreover, we analyze the space of solutions and stability of the thermal giant graviton and find that, in parallel with the extremal case, there are two available solutions for a given temperature and angular momentum, one stable and one unstable. In order to write down the equations of motion, action and conserved charges for the thermal giant graviton we present a slight generalization of the blackfold formalism for charged black branes. Finally, we also briefly consider the thermal giant graviton moving in the AdS_5 part.Comment: v1: 32 pages + 11 pages appendices, 13 figures, v2: typos fixed in Sec.2 and other misprints, references adde

Double Wick rotating Green-Schwarz strings

Via an appropriate field redefinition of the fermions, we find a set of conditions under which light cone gauge fixed world sheet theories of strings on two different backgrounds are related by a double Wick rotation. These conditions take the form of a set of transformation laws for the background fields, complementing a set of transformation laws for the metric and B field we found previously with a set for the dilaton and RR fields, and are compatible with the supergravity equations of motion. Our results prove that at least to second order in fermions, the AdS_5 x S^5 mirror model which plays an important role in the field of integrability in AdS/CFT, represents a string on `mirror AdS_5 x S^5', the background that follows from our transformations. We discuss analogous solutions for AdS_3 x S^3 x T^4 and AdS_2 x S^2 x T^6. The main ingredient in our derivation is the light cone gauge fixed action for a string on an (almost) completely generic background, which we explicitly derive to second order in fermions.Comment: v2, updated discussion on target space interpretation, elaborated discussion on minor points, content matches published version, 28 pages, 3 figure

Regular spherical dust spacetimes

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.Comment: Minor improvements, additional references. Accepted by GR

S-folds and 4d N=3 superconformal field theories

S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by Garcia-Etxebarria and Regalado to provide the first construction of four dimensional N=3 superconformal theories. In this note, we classify the different variants of these N=3 preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of N=3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.Comment: 29 pages; v2: references adde