Miracle-dz/UniFAR-FTUs huggingface dataset:
Economic Growth and the Rise of Large Firms∗

Why does the prevalence of large firms vary significantly across countries? This paper investigates the relationship between economic development and the right tail of the firm size distribution. First, I document a positive empirical relationship between GDP per capita and the right tail thickness of the firm size distribution. Then, I develop a simple idea diffusion model with endogenous growth and firm size distribution. The economy features an asymptotic balanced growth path. Along the transition, Gibrat’s law holds at each date, and the right tail of the firm size distribution becomes thicker. The firm size distribution converges to Zipf’s distribution. Despite being parsimonious, the model provides a good quantitative fit to the US GDP per capita growth. In addition, idea diffusion helps to understand the tight connection between firm growth and economic growth. In a general class of idea diffusion models, I demonstrate an equivalence between Gibrat’s law and thicker tails and between Zipf’s law and long-run growth. Lastly, I show that policies favoring large firms can improve welfare in the presence of the idea diffusion externality.
Phase Retrieval By Projections

The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in engineering: recovering a vector from measurements consisting of norms of its orthogonal projections onto a family of subspaces. There exist semidefinite programming algorithms to solve this problem, but much remains unknown for this more general case. Can families of subspaces for which such measurements are injective be completely classified? What is the minimal number of subspaces required to have injectivity? How closely does this problem compare to the usual phase retrieval problem with families of measurement vectors? In this paper, we answer or make incremental steps toward these questions. We provide several characterizations of subspaces which yield injective measurements, and through a concrete construction, we prove the surprising result that phase retrieval can be achieved with $2M-1$ projections of arbitrary rank in $\HH_M$. Finally we present several open problems as we discuss issues unique to the phase retrieval problem with subspaces.
The stretched exponential behavior and its underlying dynamics. The phenomenological approach

Abstract We show that the anomalous diffusion equations with a fractional spatial derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the Lévy stable distributions which stem from the evolution properties of stretched or compressed exponential function. The formal solutions of these fractional differential equations are found by using the evolution operator method where the evolution is conceived as integral transform whose kernel is the Green function. Exact and explicit examples of the solutions are reported and studied for various fractional order of derivatives and for different initial conditions.
Irrational Toric Varieties

Classical toric varieties are among the simplest objects in algebraic geometry. They arise in an elementary fashion as varieties parametrized by monomials whose exponents are a finite subset $\mathcal{A}$ of $\mathbb{Z}^n$. They may also be constructed from a rational fan $\Sigma$ in $\mathbb{R}^n$. The combinatorics of the set $\mathcal{A}$ or fan $\Sigma$ control the geometry of the associated toric variety. These toric varieties have an action of an algebraic torus with a dense orbit. Applications of algebraic geometry in geometric modeling and algebraic statistics have long studied the nonnegative real part of a toric variety as the main object, where the set $\mathcal{A}$ may be an arbitrary set in $\mathbb{R}^n$. These are called irrational affine toric varieties. This theory has been limited by the lack of a construction of an irrational toric variety from an arbitrary fan in $\mathbb{R}^n$. We construct a theory of irrational toric varieties associated to arbitrary fans. These are $(\mathbb{R}_>)^n$-equivariant cell complexes dual to the fan. Such an irrational toric variety is projective (may be embedded in a simplex) if and only if its fan is the normal fan of a polytope, and in that case, the toric variety is homeomorphic to that polytope. We use irrational toric varieties to show that the space of Hausdorff limits of translates an irrational toric variety associated to a finite subset $\mathcal{A}$ of $\mathbb{R}^n$ is homeomorphic to the secondary polytope of $\mathcal{A}$.
The morphology of MSS-sequences in a wide class of unimodal maps, its structure and decomposition

The MSS-sequences (U-sequences) in a wide class of unimodal maps have the look $\mathrm{P}=(\mathrm{R} \mathrm{L}^{q})^{n_1} \mathrm{S}_1(m_1,q-1) (\mathrm{R} \mathrm{L}^{q})^{n_2}\mathrm{S}_2(m_2,q-1) $ $\ldots$ $ (\mathrm{R} \mathrm{L}^{q})^{n_r}$ $ \mathrm{S}_r(m_r,q-1)\mathrm{C},$ where $\mathrm{S}_i(m_i, q-1)$ are sequences of $\mathrm{R}$s and $\mathrm{L}$s that contain at most $q-1$ consecutive $\mathrm{L}$s. The first block $\mathrm{RL}^q$ and the sequence $\mathrm{S}_1$ following it are essential for an admissible sequence to be a MSS-sequence. Moreover $\mathrm{S}_i(m_i,q-1), \ i=2, \ldots, r$ are determined by $\mathrm{S}_1(m_1,q-1)$. Explicit structure of MSS-sequences will be given as well as the theorems that decompose the non-primary MSS-sequences. The cardinality will be calculated for some important sets of non-primary MSS-sequences and an algorithm to generate the blocks $\mathrm{S}_i(m_i,q-1), \ i=1, \ldots, r$ will be provided, as the construction of the blocks $\mathrm{S}_i(m_i,q-1)$ allows the construction of the MSS-sequences.
The rate of the convergence of the mean score in random sequence comparison

We consider a general class of super-additive scores measuring the similarity of two independent sequences of $n$ i.i. d. letters from a finite alphabet. Our object of interest is the mean score by letter $l_n$. By the subadditivity $l_n$ is nondecreasing and converges to a limit $l$. We give a simple method of bounding the difference $l-l_n$ and obtaining the rate of convergence. Our result generalizes a previous result of Alexander, where only the special case of the longest common subsequence is considered.
Embedding simply connected 2-complexes in 3-space

Firstly, we characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by nine excluded minors. This answers questions of Lov\'asz, Pardon and U. Wagner. The excluded minors are the cones over $K_5$ and $K_{3,3}$, five related constructions, and the remaining two are obtained from triangulations of the M\"obius strip by attaching a disc at its central cycle. Secondly, we extend the above theorem to all simply connected 2-dimensional simplicial complexes.
Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples

We study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions, adjoints and self-adjointness of such realizations are discussed. We construct regular spectral triples $(\mathcal{A},\mathcal{H},\mathcal{D})$ for manifolds with boundary of arbitrary dimension, where $\mathcal{H}$ is the space of square integrable sections. Starting out from Dirac operators with APS-conditions, these triples are even in case of even dimensional manifolds; we show that the closure of $\mathcal{A}$ in $\mathscr{L}(\mathcal{H})$ coincides with the continuous functions on the manifold being constant on each connected component of the boundary.
Structure-Adaptive, Variance-Reduced, and Accelerated Stochastic Optimization

In this work we explore the fundamental structure-adaptiveness of state of the art randomized first order algorithms on regularized empirical risk minimization tasks, where the solution has intrinsic low-dimensional structure (such as sparsity and low-rank). Such structure is often enforced by non-smooth regularization or constraints. We start by establishing the fast linear convergence rate of the SAGA algorithm on non-strongly-convex objectives with convex constraints, via an argument of cone-restricted strong convexity. Then for the composite minimization task with a coordinate-wise separable convex regularization term, we propose and analyse a two stage accelerated coordinate descend algorithm (Two-Stage APCG). We provide the convergence analysis showing that the proposed method has a global convergence in general and enjoys a local accelerated linear convergence rate with respect to the low-dimensional structure of the solution. Then based on this convergence result, we proposed an adaptive variant of the two-stage APCG method which does not need to foreknow the restricted strong convexity beforehand, but estimate it on the fly. In numerical experiments we compare the adaptive two-stage APCG with various state of the art variance-reduced stochastic gradient methods on sparse regression tasks, and demonstrate the effectiveness of our approach.
Schemes as functors on topological rings

Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\`ele rings to any ring $R$ with a topology. This definition is functorial in both $X$ and $R$, and it does not rely on any restriction on $X$ like separability or finiteness conditions. We characterize properties of $R$, such as being a topological Hausdorff ring, a local ring or having $R^\times$ as an open subset for which inversion is continuous, in terms of functorial properties of the topology of $X(R)$. Particular instances of this general approach yield a new characterization of adelic topologies, and a definition of topologies for higher local fields.
Reading racetrack and self-graphing on reading and behavior of struggling readers with emotional behavioral disorders and learning disabilities

ABSTRACT Reading is a fundamental academic skill and influences numerous outcomes throughout lifespan. Unfortunately, many German students struggle with basic reading. Specifically, students with Learning Disabilities (LD) and Emotional Behavioural Disorders (EBD) encounter major hurdles. Consequently, insufficient reading achievement and concomitant behavioural problems diminish motivation to learn. Therefore, a multiple baseline design was used to evaluate the effects of a peer-mediated Reading Racetrack intervention with and without self-graphing on word reading, academically engaged behaviour (AEB), and disruptive behaviour (DB) of primary-school students with LD and EBD (n = 7). The procedure took place three times per week for 25 minutes over a six-week period. As a result, all students increased in reading when Racetracks without Self-Graphing was implemented, without further increases when adding Self-Graphing. There was no intervention effect on AEB in the regression analysis across phases – however, Racetracks with and without Self-Graphing showed significant effects on DB each. Moreover, students rated the intervention positively.
The cosmological constant problem in heterotic-M-theory and the orbifold of time

Chameleon fields are quantum fields with an increasing mass as a function of the matter density of the environment. Recently chameleon fields have been exploited to solve the cosmological constant problem in the Modified Fujii's Model - MFM [Phys Rev D82 (2010) 044006]. However, gravity has been treated basically at a semiclassical level in that paper. In this article the stringy origin of the MFM is further discussed: as we will see, the MFM can be obtained from heterotic-M-theory. Consequently, a quantum description of gravity is obtained and the theory is finite because we choose the string mass as our UV cut-off. This stringy origin of the MFM creates stronger theoretical grounds for our solution to the cosmological constant problem. In our analysis, time will be compactified on a $S^1/Z_2$ orbifold and this peculiar compactification of time has a number of consequences. For example, as we will see, quantum gravity and a quantum gauge theory are actually the same theory in the sense that gravity is the time-evolution of a gauge theory. This might be the key to obtain a non-approximated stabilizing potential for the dilaton in the string frame. In this paper we will further discuss the non-equivalence of different conformal frames at the quantum level. As we will see, in our approach we use basically a unique conformal frame: the frame where the masses of particles are field dependent. A word of caution is necessary: we do not take into account massive string states and IR divergences.
Non-Markovian decoherent quantum walks

Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker's behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.
Modified flower pollination algorithm for an off-grid solar photovoltaic system

This Operating the solar photovoltaic (PV) system at its maximum power point (MPP) under numerous environmental conditions to extract the maximum power is a challenging task. The challenge is to track the MPP, especially under partial shading conditions (PSC), where the formation of multiple MPP occurs in the characteristic curve of a PV array. Nevertheless, achieving this would benefit us with optimal power production, reducing the payback time and initial cost of the PV system. To perform this duty, an electronic circuit ruled by an algorithm is employed. The MPP tracking (MPPT) algorithms can be categorized into conventional and nature inspired. The conventional algorithms can successfully track the MPP under uniform weather conditions (UWC), and unable to identify the global MPP (GMPP) under PSC. However, the nature inspired algorithms possess the ability to perform efficiently under all weather conditions. Considering this strength of nature inspired algorithms, one of the top performing algorithms named as Flower pollination algorithm (FPA) is selected based on its brilliant searching strategy in adjacent and distant locations. In this paper, some structural modifications have been proposed in the FPA to further improve its searching capability and get more quick, accurate and efficient results for the MPPT of solar PV system. Results have proven the superiority of the proposed Modified FPA (MFPA) over the FPA in terms of efficiency, accuracy, tracking speed, energy conservation, economic saving, and payback time. Simulation is performed in MATLAB/Simulink.
Cultivation conditions and biochemical characterization of the proteolytic enzymes with fibrinolytic action obtained from mushrooms in the last ten years

Fibrinolytic enzymes are proteases that are capable of degrading the fibrin mesh present in blood clots and can be obtained through fungal extracts. Thus, the objective of this paper was to seek out and compare all the information regarding the production and biochemical characterization of fibrinolytic enzymes of mushroom species published in papers in the last ten years. The research was carried out in eight national and international electronic databases using the terms: “fungal enzymes”, “fibrinolytic Proteases”, “thrombosis” and “mushrooms”. The results obtained were analyzed according to each step. In the first stage, the titles and abstracts of all papers were analyzed independently; in the second stage, all papers were read and those that did not meet the inclusion criteria were excluded. Then, the remaining papers were reviewed and the data were tabulated and compared. As a result, it was found that enzymes with fibrinolytic action were obtained from eight species of mushrooms in the period of this research: P. sajor-cashew, P. ferulae, P. ostreatus, L. shimeji, A. polytricha, H. erinaceum, C. comatus and C. militaris. The enzymes were identified as protease SPPs, metalloproteases, serine proteases and serine metalloproteases. The methods used to evaluate fibrinolytic activity were the fibrin plate method and/or the formation of artificial thrombus through thrombin and fibrinogen. The molecular mass of these enzymes ranged from ~18 to 66 kDa and, for the biochemical characterization of the extracts, the pH ranged from 4.0 to 9.5 and the optimum temperature from 25 to 70 ºC. Via the review, it was observed that few articles were published on the subject in question, which made it necessary to carry out more studies to discover the biotechnological properties of mushrooms and define their applications in the most diverse sectors of industries, not only in commercial species of mushrooms, but also in native species.
The Quality of Investigation Audit Influenced by Independence and Integrity

Quality audits are important not only for investigators but also for auditors when advancing as experts in court. Therefore, the formation of MIA to handle investigative examinations is BPK's answer to the phenomena that occur in society related to the quality of the results of BPK investigations. However, even after the formation of MIA, there were still complaints from the public regarding the quality of the results of investigative examinations. BPK received a lot of attention because of actions that were not in accordance with the BPK auditors' code of ethics, namely integrity violations that resulted in arrest by law enforcers and undergoing trial at the Corruption Court. For this reason, auditors must always maintain an attitude of mental independence, in all matters relating to the provision of audit services, to improve audit quality. This study aims to analyze how independence and integrity can increase the quality of investigation audit. This study involved 267 investigators of Law Enforcement Agencies as respondents using a questionnaire. Furthermore, the data were analyzed using descriptive statistical analysis and SEM techniques. The results of this study provide empirical evidence that independence and integrity have a significant positive effect on the quality of investigation audit.
Gains from Trade and the Food Engel Curve

IZA DP No. 15674 OCTOBER 2022 Gains from Trade and the Food Engel Curve* This paper examines the extent to which gains-from-trade predictions from commonlyused trade theories are consistent with observed household consumption decisions. Our approach is based on inference from household-level estimation of food Engel curves in the US and in a few other countries. For a given price index as the deflator of income, deviations from food Engel curves indicate how biased that price index is relative to the true household price index. We construct open-economy price indices based on trade theory and data, evaluate their biases according to our approach, and compare them with the bias of official CPI statistics. We find that theory-consistent open-economy price indices that account for industry-level heterogeneity and input-output linkages tend to eliminate a large fraction of the bias of CPI. JEL Classification: D12, F14, E31
The Fredholm index for operators of tensor product type

We consider pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators, which are defined on the product manifold $M_1 \times M_2$ for closed manifolds $M_1$ and $M_2$. We prove a topological index theorem for Fredholm operators of tensor product type. To this end we construct a suitable double deformation groupoid and prove a Poincare duality type result in relative $K$-theory.
Universal equations and constants of turbulent motion

This paper presents a parameter-free theory of shear-generated turbulence at asymptotically high Reynolds numbers in incompressible fluids. It is based on a two-fluids concept. Both components are materially identical and inviscid. The first component is an ensemble of quasi-rigid dipole-vortex tubes (vortex filaments, excitations) as quasi-particles in chaotic motion. The second is a superfluid performing evasive motions between the tubes. The local dipole motions follow Helmholtz' law. The vortex radii scale with the energy-containing length scale. Collisions between quasi-particles lead either to annihilation (likewise rotation, turbulent dissipation) or to scattering (counterrotation, turbulent diffusion). There are analogies with birth and death processes of population dynamics and their master equations and with Landau's two-fluid theory of liquid helium. For free homogeneous decay the theory predicts the turbulent kinetic energy to follow t−1. With an adiabatic wall condition it predicts the logarithmic law with von Kármán's constant as . Likewise rotating couples form localized dissipative patches almost at rest (→ intermittency) wherein under local quasi-steady conditions the spectrum evolves into an ‘Apollonian gear’ as discussed first by Herrmann (1990 Correlation and Connectivity (Dordrecht: Kluwer) pp 108–20). Dissipation happens exclusively at scale zero and at finite scales this system is frictionless and reminds of Prigogine's (1947 Etude Thermodynamique des Phenomenes Irreversibles (Liege: Desoer) p 143) law of minimum (here: zero) entropy production. The theory predicts further the prefactor of the 3D-wavenumber spectrum (a Kolmogorov constant) as , well within the scatter range of observational, experimental and direct numerical simulation results.
Study of a degenerate reaction-diffusion system arising in particle dynamics with aggregation effects

In this paper we are interested in a degenerate parabolic system of reaction-diffusion equations arising in biology when studying cell adhesion at the protein level. In this modeling the unknown is the couple of the distribution laws of the freely diffusing proteins and of the fixed ones. Under sufficient conditions on the aggregation and unbinding probabilities, we prove the existence of solution of the considered system, as well as their positivity, boundedness and uniqueness. Moreover, we discuss the stability of the equilibrium solution. Finally, we show that the simpler and particular choice of an affine aggregation function and of a constant unbinding probability do not lead to pattern formation as expected in the application. These analytical results are also supported by some numerical simulation.