ABSTRACT Financial reports, including 10-K and 10-Q filings, are a primary source of textual data in business disciplines. However, extracting specific sections from these lengthy documents remains a challenge. Custom code development by each research team to parse these files leads to redundancy, inefficiency, and inconsistencies and is especially challenging for teams lacking technical expertise. We address this by offering raw textual data from MD&A, risk factors, and business description sections, and financial statement notes, for all firms from 2008 onward. We share Python code to facilitate download and parsing. We also provide pre-calculated textual metrics, such as word counts, readability measures, and several bags of word metrics, including negative sentiment, forward-looking statements, and R&D. Additionally, we contribute two new word lists, COVID-19 and human capital, developed using a novel approach based on disclosure shocks. Our goal is to streamline research processes, ensure consistency, and enable further advances in the field. Data Availability: Data are available for download at http://www.analytext.com/. Code is available for download at https://github.com/mmcodesso/edgar-metrics-parser JEL Classifications: C55; C88; M4; M48.

For a finitely generated LEF group Gamma , we study the orders of finite groups admitting local embeddings of balls in a word metric on Gamma , as measured by the LEF growth function. We prove that any sufficiently smooth increasing function between n! and exp (exp (n)) is close to the LEF growth function of some finitely generated group. This is achieved by estimating the LEF growth of some semidirect products of the form {{,textrm{FSym},}}(Omega ) rtimes Gamma , where Omega curvearrowleft Gamma is an appropriate transitive action and {{,textrm{FSym},}}(Omega ) is the group of finitely supported permutations of Omega . A key tool in the proof is to identify sequences of finitely presented subgroups with short “relative” presentations. In a similar vein, we also obtain estimates on the LEF growth of some groups of the form E_{Omega } (R) rtimes Gamma , for R an appropriate unital ring and E_{Omega } (R) the subgroup of {{,textrm{Aut},}}_R (R[Omega ]) generated by all transvections with respect to basis Omega .

We give a new, short proof of a result of Virk, that the Vietoris–Rips complex of the group Z n \mathbb {Z}^n with the standard word metric is contractible at large enough scales. This is inspired by a key observation in Virk’s proof, but we use Bestvina–Brady discrete Morse theory to get a very short proof with better bounds. In the course of this, we get a new, general criterion for a metric space to have contractible Vietoris–Rips complexes at large enough scales, which could prove useful in the future.

In this paper, we consider wreath products of the form [Formula: see text] where [Formula: see text] is finite and simple. We compute word metrics in these groups and show that under these metrics the groups have the metric version LEF.

Abstract We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics associated with finite generating sets is a quasi-isometry if and only if it is an isomorphism.

We prove that for each positive integer n n , the Rips complexes of the n n -dimensional integer lattice in the d 1 d_1 metric (i.e., the Manhattan metric, also called the natural word metric in the Cayley graph) are contractible at scales above n 2 ( 2 n − 1 ) n^2(2n-1) , with the bounds arising from the Jung constants. We introduce a new concept of locally dominated vertices in a simplicial complex, upon which our proof strategy is based. This allows us to deduce the contractibility of the Rips complexes from a local geometric condition called local crushing. In the case of the integer lattices in dimension n n and a fixed scale r r , this condition entails the comparison of finitely many distances to conclude that the corresponding Rips complex is contractible. In particular, we are able to verify that for n = 1 , 2 , 3 n=1,2,3 , the Rips complex of the n n -dimensional integer lattice at scale greater or equal to n n is contractible. We conjecture that the same proof strategy can be used to extend this result to all dimensions n n .

We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group.More precisely, for any proper geodesic metric space X and any sublinear function , we construct a boundary for X , denoted by @ X , that is quasi-isometrically invariant and metrizable.As an application, we show that when G is the mapping class group of a finite type surface or a relatively hyperbolic group, with minimal assumptions, the Poisson boundary of G can be realized on the -Morse boundary of G equipped with the word metric associated to any finite generating set.

We prove that finite index subgroups in [Formula: see text]-arithmetic Chevalley groups are bounded.

The paper studies the Hausdorff dimension of harmonic measures on various boundaries of a relatively hyperbolic group which are associated with random walks driven by a probability measure with finite first moment. With respect to the Floyd metric and the shortcut metric, we prove that the Hausdorff dimension of the harmonic measure equals the ratio of the entropy and the drift of the random walk.If the group is infinitely-ended, the same dimension formula is obtained for the end boundary endowed with a visual metric. In addition, the Hausdorff dimension of the visual metric is identified with the growth rate of the word metric. These results are complemented by a characterization of doubling visual metrics for accessible infinitely-ended groups: the visual metrics on the end boundary is doubling if and only if the group is virtually free. Consequently, there are at least two different bi-Hölder classes (and thus quasi-symmetric classes) of visual metrics on the end boundary.

Colimit theorems for coarse coherence with applications

Classifying decomposition and wavelet coorbit spaces using coarse geometry

Recurrent Neural Networks (RNNs) have become important tools for tasks such as speech recognition, text generation, or natural language processing. However, their inference may involve up to billions of operations and their large number of parameters leads to large storage size and runtime memory usage. These reasons impede the adoption of these models in real-time, on-the-edge applications. Field-Programmable Gate Arrays (FPGAs) and Application-Specific Integrated Circuits (ASICs) have emerged as promising solutions for the hardware acceleration of these algorithms, thanks to their degree of customization of compute data paths and memory subsystems, which makes them take the maximum advantage from compression techniques for what concerns area, timing, and power consumption. In contrast to the extensive study in compression and quantization for plain feed forward neural networks in the literature, little attention has been paid to reducing the computational resource requirements of RNNs. This work proposes a new effective methodology for the post-training quantization of RNNs. In particular, we focus on the quantization of Long Short-Term Memory (LSTM) RNNs and Gated Recurrent Unit (GRU) RNNs. The proposed quantization strategy is meant to be a detailed guideline toward the design of custom hardware accelerators for LSTM/GRU-based algorithms to be implemented on FPGA or ASIC devices using fixed-point arithmetic only. We applied our methods to LSTM/GRU models pretrained on the IMDb sentiment classification dataset and Penn TreeBank language modelling dataset, thus comparing each quantized model to its floating-point counterpart. The results show the possibility to achieve up to 90% memory footprint reduction in both cases, obtaining less than 1% loss in accuracy and even a slight improvement in the Perplexity per word metric, respectively. The results are presented showing the various trade-offs between memory footprint reduction and accuracy changes, demonstrating the benefits of the proposed methodology even in comparison with other works from the literature.

We study the speed of convergence to the asymptotic cone for a finitely generated nilpotent group endowed with a word metric. The first result on this theme is given by Burago who showed that an abelian group endowed with a word metric converges to the normed space with the speed \(O\left( \frac{1}{n}\right) \) in the sense of Gromov–Hausdorff distance. Later Krat showed the same statement for the Heisenberg group, and Breuillard and Le Donne constructed an example, the direct product of the \(\mathbb {Z}\) and the Heisenberg group with a specific word metric, whose speed of convergence is precisely \(O\left( \frac{1}{\sqrt{n}}\right) \). For 2-step nilpotent groups, we show that if the asymptotic cone is non-singular, then the speed of convergence is \(O\left( \frac{1}{n}\right) \) for any choice of generating set. Our argument can be applied to every nilpotent Lie group with a left-invariant sub-Finsler metric. In terms of sub-Finsler geometry, the condition being non-singular is equivalent to the strongly bracket generating condition, and also to absence of abnormal curves.

We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geodesics, while the second one as their scarcity. We discuss examples for both cases.

Abstract We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those that arise as asymptotic cones of word metrics, on the Heisenberg group. We develop theory for the more general case of horofunction boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives of the distance function.

We are interested in the Guivarc’h inequality for admissible random walks on finitely generated relatively hyperbolic groups, endowed with a word metric. We show that for random walks with finite super-exponential moment, if this inequality is an equality, then the Green distance is roughly similar to the word distance, generalizing results of Blachère, Haïssinsky, and Mathieu for hyperbolic groups [4]. Our main applications are for relatively hyperbolic groups with some virtually abelian parabolic subgroup of rank at least 2, relatively hyperbolic groups with spherical Bowditch boundary, and free products with at least one virtually nilpotent factor. We show that for such groups, the Guivarc’h inequality with respect to a word distance and a finitely supported random walk is always strict.

Abstract Given a countably infinite group G acting on some space X, an increasing family of finite subsets Gn , x∈ X and a function f over X we consider the sums Sn (f, x) = ∑ g∈Gnf(gx). The asymptotic behaviour of Sn (f, x) is a delicate problem that was studied under various settings. In the following paper we study this problem when G is a specific lattice in SL (2, ℤ ) acting on the projective line and Gn are chosen using the word metric. The asymptotic distribution is calculated and shown to be tightly connected to Minkowski’s question mark function. We proceed to show that the limit distribution is stationary with respect to a random walk on G defined by a specific measure µ. We further prove a stronger result stating that the asymptotic distribution is the limit point for any probability measure over X pushed forward by the convolution power µ∗n .

We introduce the notion of \emph{joint spectrum} of a compact set of matrices $S \subset GL_d(\mathbb{C})$, which is a multi-dimensional generalization of the joint spectral radius. We begin with a thorough study of its properties (under various assumptions: irreducibility, Zariski-density, domination). Several classical properties of the joint spectral radius are shown to hold in this generalized setting and an analogue of the Lagarias-Wang finiteness conjecture is discussed. Then we relate the joint spectrum to matrix valued random processes and study what points of it can be realized as Lyapunov vectors. We also show how the joint spectrum encodes all word metrics on reductive groups. Several examples are worked out in detail.

We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e., they have full density with respect to counting in balls for the word metric in the Cayley graph) and translation length grows linearly. We provide applications to a large class of relatively hyperbolic groups and graph products, including all right-angled Artin groups and right-angled Coxeter groups.

We consider a finitely generated group endowed with a word metric. The group acts on itself by isometries, which induces an action on its horofunction boundary. The conjecture is that nilpotent groups act trivially on their reduced boundary. We will show this for the Heisenberg group. The main tool will be a discrete version of the isoperimetric inequality.