Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block

The Gauß hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gauß hypergeometric function is slightly “off-shell”.

A System for the Inclusion of the Informal Recycling Sector (IRS) in Mexico City’s Solid Waste Management

With 19 million inhabitants, Mexico City is the most populated agglomeration in Latin America, concentrating 30% of the national population. More than 61% of municipal solid waste (MSW) is sent to landfills, and 13% of MSW is recovered by Informal Sector Recyclers (ISRs) for recycling, which is the most crucial treatment option in the city. This article adopts a systemic approach to addressing the problem of the operationalization of relationships between ISRs and public services in Mexico City to design a recursive organizational structure with the identification of the critical roles and functions of management and governance in multi-level and multi-stakeholder relationships to integrate ISRs into MSW management. Using the Viable System Model (VSM) recursive structure to propose functional organizational structures in Mexico City is a new route for the study and application of systemic thinking in ISR integration. The VSM of the recycling system in Mexico City considers the recycling activities and characteristics of the territory at each recursion level. The authorities of the corresponding hierarchical level, who have sufficient knowledge of the physical and socioeconomic characteristics of the territory, are responsible for the design and operations.

Compositional learning of mutually recursive procedural systems

This paper presents a compositional approach to active automata learning of Systems of Procedural Automata (SPAs), an extension of Deterministic Finite Automata (DFAs) to systems of DFAs that can mutually call each other. SPAs are of high practical relevance, as they allow one to efficiently learn intuitive recursive models of recursive programs after an easy instrumentation that makes calls and returns observable. Key to our approach is the simultaneous inference of individual DFAs for each of the involved procedures via expansion and projection: membership queries for the individual DFAs are expanded to membership queries of the entire SPA, and global counterexample traces are transformed into counterexamples for the DFAs of concerned procedures. This reduces the inference of SPAs to a simultaneous inference of the DFAs for the involved procedures for which we can utilize various existing regular learning algorithms. The inferred models are easy to understand and allow for an intuitive display of the procedural system under learning that reveals its recursive structure. We implemented the algorithm within the LearnLib framework in order to provide a ready-to-use tool for practical application which is publicly available on GitHub for experimentation.

Alternate Lucas Cubes

We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci cubes and have a useful fundamental decomposition similar to the one for Fibonacci cubes. The vertices of alternate Lucas cubes are constructed from binary strings that are encodings of Lucas representation of integers. As well as ordinary hypercubes, Fibonacci cubes and Lucas cubes, alternate Lucas cubes have several interesting structural and enumerative properties. In this paper we study some of these properties. Specifically, we give the fundamental decomposition giving the recursive structure, determine the number of edges, number of vertices by weight, the distribution of the degrees; as well as the properties of induced hypercubes, [Formula: see text]-cube polynomials and maximal hypercube polynomials. We also obtain the irregularity polynomials of this family of graphs, determine the conditions for Hamiltonicity, and calculate metric properties such as the radius, diameter, and the center.

Entry-Proofness and Discriminatory Pricing under Adverse Selection

This paper studies competitive allocations under adverse selection. We first provide a general necessary and sufficient condition for entry on an inactive market to be unprofitable. We then use this result to characterize, for an active market, a unique budget-balanced allocation implemented by a market tariff making additional trades with an entrant unprofitable. Motivated by the recursive structure of this allocation, we finally show that it emerges as the essentially unique equilibrium outcome of a discriminatory ascending auction. These results yield sharp predictions for competitive nonexclusive markets. (JEL D11, D43, D82, D86)

Continuous phase transitions on Galton–Watson trees

Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton–Watson trees. For example, let $\mathcal{T}_1$ be the event that a Galton–Watson tree is infinite and let $\mathcal{T}_2$ be the event that it contains an infinite binary tree starting from its root. These events satisfy similar recursive properties: $\mathcal{T}_1$ holds if and only if $\mathcal{T}_1$ holds for at least one of the trees initiated by children of the root, and $\mathcal{T}_2$ holds if and only if $\mathcal{T}_2$ holds for at least two of these trees. The probability of $\mathcal{T}_1$ has a continuous phase transition, increasing from 0 when the mean of the child distribution increases above 1. On the other hand, the probability of $\mathcal{T}_2$ has a first-order phase transition, jumping discontinuously to a non-zero value at criticality. Given the recursive property satisfied by the event, we describe the critical child distributions where a continuous phase transition takes place. In many cases, we also characterise the event undergoing the phase transition.

Alignments of biomolecular contact maps

Alignments of discrete objects can be constructed in a very general setting as super-objects from which the constituent objects are recovered by means of projections. Here, we focus on contact maps, i.e. undirected graphs with an ordered set of vertices. These serve as natural discretizations of RNA and protein structures. In the general case, the alignment problem for vertex-ordered graphs is NP-complete. In the special case of RNA secondary structures, i.e. crossing-free matchings, however, the alignments have a recursive structure. The alignment problem then can be solved by a variant of the Sankoff algorithm in polynomial time. Moreover, the tree or forest alignments of RNA secondary structure can be understood as the alignments of ordered edge sets.

Single-frame super-resolution for remote sensing images based on improved deep recursive residual network

Single-frame image super-resolution (SISR) technology in remote sensing is improving fast from a performance point of view. Deep learning methods have been widely used in SISR to improve the details of rebuilt images and speed up network training. However, these supervised techniques usually tend to overfit quickly due to the models’ complexity and the lack of training data. In this paper, an Improved Deep Recursive Residual Network (IDRRN) super-resolution model is proposed to decrease the difficulty of network training. The deep recursive structure is configured to control the model parameter number while increasing the network depth. At the same time, the short-path recursive connections are used to alleviate the gradient disappearance and enhance the feature propagation. Comprehensive experiments show that IDRRN has a better improvement in both quantitation and visual perception.

Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-body Systems

This article presents methods to efficiently compute the Coriolis matrix and underlying Christoffel symbols (of the first kind) for tree-structure rigid-body systems. The algorithms can be executed purely numerically, without requiring partial derivatives as in unscalable symbolic techniques. The computations share a recursive structure in common with classical methods such as the Composite-Rigid-Body Algorithm and are of the lowest possible order: $O(Nd)$ for the Coriolis matrix and $O(Nd^2)$ for the Christoffel symbols, where $N$ is the number of bodies and $d$ is the depth of the kinematic tree. Implementation in C/C++ shows computation times on the order of 10-20 $\mu$s for the Coriolis matrix and 40-120 $\mu$s for the Christoffel symbols on systems with 20 degrees of freedom. The results demonstrate feasibility for the adoption of these algorithms within high-rate (>1kHz) loops for model-based control applications.