Default Invariance: Naïve Category of Law and Finance

Default invariance is the idea that default does not change at any scale of law and finance. Default is a conserved quantity in a universe where fundamental principles of law and finance operate. It exists at the micro-level as part of the fundamental structure of every financial transaction, and at the macro- level, as a fixed critical point within the relatively stable phases of the law and finance cycle. A key point is that default is equivalent to maximizing uncertainty at the micro-level and at the macro-level, is equivalent to the phase transition where unbearable fluctuations occur in all forms of risk transformation, including maturity, liquidity and credit. As such, default invariance is the glue that links the micro and macro structures of law and finance. In this essay, we apply naïve category theory (NCT), a type of mapping logic, to these types of phenomena. The purpose of using NCT is to introduce a rigorous (but simple) mathematical methodology to law and finance discourse and to show that these types of structural considerations are of prime practical importance and significance to law and finance practitioners. These mappings imply a number of novel areas of investigation. From the micro- structure, three macro-approximations are implied. These approximations form the core analytical framework which we will use to examine the phenomena and hypothesize rules governing law and finance. Our observations from these approximations are grouped into five findings. While the entirety of the five findings can be encapsulated by the three approximations, since the intended audience of this paper is the non-specialist in law, finance and category theory, for ease of access we will illustrate the use of the mappings with relatively common concepts drawn from law and finance, focusing especially on financial contracts, derivatives, Shadow Banking, credit rating agencies and credit crises.

Temporary contracts and non-protected employment in Argentina, Chile and Perú: incidence and determinants

The diverse kinds of legal temporary contracts and the employment forms that do not comply with legal requirements both facilitate employment adjustment to firms´ requirements and entail labour cost reductions. Their employment incidence depends not only on the economic and labour market evolutions but also on other factors, in particular the historical trajectories followed by labour legislation, state enforcement, and the degree of compliance. To contribute to the understanding of the determinants of the degree of utilization of different employment practices, the study reported in this article explores the use made of the various legal temporary contracts and of precarious employment relationships by private enterprises in three Latin American countries (Argentina, Chile and Peru) during 2003-2012, a period of economic growth, and the explanatory role of diverse factors.

Regulating Vertical Agreements: A Comparative Law & Economics analysis of Brazil and Europe

This PhD thesis discusses antitrust enforcement of anti-competitive vertical agreements in Europe and in Brazil from an institutional perspective. It considers both the evolution of the legal framework and the application of the existing policies, with the analysis of case studies. The research highlights the main challenges of the current approaches adopted by the competition authorities in these jurisdictions and formulates specific proposals for future improvements. Because the Brazilian competition rules were originally inspired by the European legal framework, this thesis also summarizes the contemporary discussions regarding comparative law and the efficiency of transplanting laws and good practices. In a Law & Economics perspective, vertical agreements have always been a paradoxical topic and constitute one of the most dynamic disputes for antitrust enforcement. The reason for that concern is the fact that those contracts among companies are complex in nature. Taking into account this background, the thesis provides an original analysis of the pro- and anti-competitive effects of vertical agreements, based on the classical literature of Law & Economics. One of the novelties of the research is the extension of the economic analysis of vertical agreements to also consider new forms of contractual abuses in the context of digital markets, such as the contractual restrictions that are being put I practice in e-commerce platforms. The international comparative approach focuses on the Brazilian and European experiences, and opens up a reflection about the policy recommendations applied to several countries with similar economic and institutional realities.

Neural Machine Translation in the Field of Law. Analysis and Evaluation against Human Reference of NMT Raw Outputs of an Atto Costitutivo of S.r.l. from Italian into German.

Artificial Intelligence (AI) is gaining ever more ground in every sphere of human life, to the point that it is now even used to pass sentences in courts. The use of AI in the field of Law is however deemed quite controversial, as it could provide more objectivity yet entail an abuse of power as well, given that bias in algorithms behind AI may cause lack of accuracy. As a product of AI, machine translation is being increasingly used in the field of Law too in order to translate laws, judgements, contracts, etc. between different languages and different legal systems. In the legal setting of Company Law, accuracy of the content and suitability of terminology play a crucial role within a translation task, as any addition or omission of content or mistranslation of terms could entail legal consequences for companies. The purpose of the present study is to first assess which neural machine translation system between DeepL and ModernMT produces a more suitable translation from Italian into German of the atto costitutivo of an Italian s.r.l. in terms of accuracy of the content and correctness of terminology, and then to assess which translation proves to be closer to a human reference translation. In order to achieve the above-mentioned aims, two human and automatic evaluations are carried out based on the MQM taxonomy and the BLEU metric. Results of both evaluations show an overall better performance delivered by ModernMT in terms of content accuracy, suitability of terminology, and closeness to a human translation. As emerged from the MQM-based evaluation, its accuracy and terminology errors account for just 8.43% (as opposed to DeepL’s 9.22%), while it obtains an overall BLEU score of 29.14 (against DeepL’s 27.02). The overall performances however show that machines still face barriers in overcoming semantic complexity, tackling polysemy, and choosing domain-specific terminology, which suggests that the discrepancy with human translation may still be remarkable.

Visual demonstration of the ionic strength effect in the classroom: the Debye-Hückel limiting law

The effects of ionic strength on ions in aqueous solutions are quite relevant, especially for biochemical systems, in which proteins and amino acids are involved. The teaching of this topic and more specifically, the Debye-Hückel limiting law, is central in chemistry undergraduate courses. In this work, we present a description of an experimental procedure based on the color change of aqueous solutions of bromocresol green (BCG), driven by addition of electrolyte. The contribution of charge product (z+|z-|) to the Debye-Hückel limiting law is demonstrated when the effects of NaCl and Na2SO4 on the color of BCG solutions are compared.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Precise determination of quantum critical points by the violation of the entropic area law

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two-dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so-called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and noncritical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.

Darcy`s law and the differential equation of motion

This note addresses the relation between the differential equation of motion and Darcy`s law. It is shown that, in different flow conditions, three versions of Darcy`s law can be rigorously derived from the equation of motion.

Scaling of structures subject to impact loads when using a power law constitutive equation

It is well known that structures subjected to dynamic loads do not follow the usual similarity laws when the material is strain rate sensitive. As a consequence, it is not possible to use a scaled model to predict the prototype behaviour. In the present study, this problem is overcome by changing the impact velocity so that the model behaves exactly as the prototype. This exact solution is generated thanks to the use of an exponential constitutive law to infer the dynamic flow stress. Furthermore, it is shown that the adopted procedure does not rely on any previous knowledge of the structure response. Three analytical models are used to analyze the performance of the technique. It is shown that perfect similarity is achieved, regardless of the magnitude of the scaling factor. For the class of material used, the solution outlined has long been sought, inasmuch as it allows perfect similarity for strain rate sensitive structures subject to impact loads. (C) 2009 Elsevier Ltd. All rights reserved.

On the Steinmetz hysteresis law

The behavior of the Steinmetz coefficient has been described for several different materials: steels with 3.2% Si and 6.5% Si, MnZn ferrite and Ni-Fe alloys. It is shown that, for steels, the Steinmetz law achieves R(2)> 0.999 only between 0.3 and 1.2 T, which is the interval where domain wall movement dominates. The anisotropy of Steinmetz coefficient for non-oriented (NO) steel is also discussed. It is shown that for a NO 3.2% Si steel with a strong Goss component in texture, the power law coefficient and remanence decreases monotonically with the direction of measurement going from rolling direction (RD) to transverse direction (TD), although coercive field increased. The remanence behavior can be related to the minimization of demagnetizing field at the surface grains. The data appear to indicate that the Steinmetz coefficient increases as magnetocrystalline anisotropy constant decreases. (c) 2008 Elsevier B.V. All rights reserved.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

Bayesian ratemaking procedure of crop insurance contracts with skewed distribution

Over the years, crop insurance programs became the focus of agricultural policy in the USA, Spain, Mexico, and more recently in Brazil. Given the increasing interest in insurance, accurate calculation of the premium rate is of great importance. We address the crop-yield distribution issue and its implications in pricing an insurance contract considering the dynamic structure of the data and incorporating the spatial correlation in the Hierarchical Bayesian framework. Results show that empirical (insurers) rates are higher in low risk areas and lower in high risk areas. Such methodological improvement is primarily important in situations of limited data.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Parametric and nonparametric statistical modelling of crop yield: implications for pricing crop insurance contracts

This article considers alternative methods to calculate the fair premium rate of crop insurance contracts based on county yields. The premium rate was calculated using parametric and nonparametric approaches to estimate the conditional agricultural yield density. These methods were applied to a data set of county yield provided by the Statistical and Geography Brazilian Institute (IBGE), for the period of 1990 through 2002, for soybean, corn and wheat, in the State of Paran. In this article, we propose methodological alternatives to pricing crop insurance contracts resulting in more accurate premium rates in a situation of limited data.

On compliance of business processes with business contracts

This paper addresses the problem of ensuring compliance of business processes, implemented within and across organisational boundaries, with the constraints stated in related business contracts. In order to deal with the complexity of this problem we propose two solutions that allow for a systematic and increasingly automated support for addressing two specific compliance issues. One solution provides a set of guidelines for progressively transforming contract conditions into business processes that are consistent with contract conditions thus avoiding violation of the rules in contract. Another solution compares rules in business contracts and rules in business processes to check for possible inconsistencies. Both approaches rely on a computer interpretable representation of contract conditions that embodies contract semantics. This semantics is described in terms of a logic based formalism allowing for the description of obligations, prohibitions, permissions and violations conditions in contracts. This semantics was based on an analysis of typical building blocks of many commercial, financial and government contracts. The study proved that our contract formalism provides a good foundation for describing key types of conditions in contracts, and has also given several insights into valuable transformation techniques and formalisms needed to establish better alignment between these two, traditionally separate areas of research and endeavour. The study also revealed a number of new areas of research, some of which we intend to address in near future.