Tevelev degrees and Hurwitz moduli spaces

We interpret the degrees which arise in Tevelev’s study of scattering amplitudes in terms of moduli spaces of Hurwitz covers. Via excess intersection theory, the boundary geometry of the Hurwitz moduli space yields a simple recursion for the Tevelev degrees (together with their natural two parameter generalisation). We find exact solutions which specialise to Tevelev’s formula in his cases and connect to the projective geometry of lines and Castelnuovo’s classical count of $g^1_d$ ’s in other cases. For almost all values, the calculation of the two parameter generalisation of the Tevelev degree is new. A related count of refined Dyck paths is solved along the way.

Revisiting a Classic Identity That Implies the Rogers–Ramanujan Identities II

We give a new proof of an identity due to Ramanujan. From this identity, he deduced the famous Rogers–Ramanujan identities. We prove this identity by establishing a simple recursion Jk=qkJk−1, where |q|<1. This is a sequel to our recent work.

Finite Controllability for Ontology-Mediated Query Answering of CRPQ

Finite ontology mediated query answering (FOMQA) is the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We study the property of finite-controllability, that is, whether FOMQA and OMQA are equivalent, for fragments of C2RPQ. C2RPQ is the language of conjunctive two-way regular path queries, which can be regarded as the result of adding simple recursion to Conjunctive Queries. For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finitely controllable and non-finitely controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finitely controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.

A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns

We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Conditions for stationarity and expressions for the moments of the process are derived. A Lagrange Multiplier test against misspecification of the within-regime correlation dynamics is proposed, and a simple recursion for multi-step-ahead conditional covariance matrices is deduced. We use this methodology to model the dynamics of the joint distribution of global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markov-switching time series models. Specifications with Student’stinnovations dominate their Gaussian counterparts both in- and out-of-sample. The dominating specification appears to be a two-regime Student’stprocess with correlations which are higher in the turbulent (high-volatility) regime.

Water Hammer (With FSI): Exact Solution — Parallelization and Application

The 1D fully coupled Fluid-Structure Interaction (FSI) model can adequately describe the water hammer effect on the fluid, and the structural behaviour of the pipe. This paper attempts to increase the capability of using an exact solution of the 1D FSI problem applied to a straight pipe with a valve. The work builds upon a simple recursion algorithm to obtain exact solutions. This paper describes the attempts to parallelize the time-consuming algorithm and presents an optimization case study. The algorithm has been parallelized using a Master-Slave MPI model for scalability. The applicability of this all has been explored by an optimization case study, which seeks the optimal damping coefficient of a dashpot connected to the valve to reduce the structural stresses in the pipe wall and the pressure in the fluid. Thus, an external damper is used to mitigate internal fluid transients.

Exact Computation of the Axial Vibration of Two Coupled Liquid-Filled Pipes

A simple recursion is presented that finds exact solutions to the problem of two coupled axially-vibrating liquid-filled pipes. Fluid-structure interaction at pipe ends and junction, and along the pipe because of axial-radial Poisson contraction, is taken into account. The solutions obtained for a waterhammer problem show unprecedented details that resemble noise.