On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

On the Computational Complexity of Measuring Global Stability of Banking Networks

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic

Reduction of systemic risk by means of Pigouvian taxation

We analyze the possibility of reduction of systemic risk in financial markets through Pigouvian taxation of financial institutions, which is used to support the rescue fund. We introduce the concept of the cascade risk with a clear operational definition as a subclass and a network related measure of the systemic risk. Using financial networks constructed from real Italian money market data and using realistic parameters, we show that the cascade risk can be substantially reduced by a small rate of taxation and by means of a simple strategy of the money transfer from the rescue fund to interbanking market subjects. Furthermore, we show that while negative effects on the return on investment (ROI) are direct and certain, an overall positive effect on risk adjusted return on investments (ROIRA) is visible. Please note that the taxation is introduced as a monetary/regulatory, not as a _scal measure, as the term could suggest. The rescue fund is implemented in a form of a common reserve fund

Gross hematuria caused by a congenital intrarenal arteriovenous malformation: a case report

<p>Abstract</p> <p>Introduction</p> <p>We report the case of a woman who presented with gross hematuria and was treated with a percutaneous embolization.</p> <p>Case presentation</p> <p>A 48-year-old Caucasian woman presented with gross hematuria, left flank pain, and clot retention. The patient had no history of renal trauma, hypertension, urolithiasis, or recent medical intervention with percutaneous instrumentation. The patient did not report any bleeding disorder and was not taking any medication. Her systolic and diastolic blood pressure values were normal at presentation. The patient had anemia (8 mg/dL) and tachycardia (110 bpm). She underwent color and spectral Doppler sonography, multi-slice computed tomography, and angiography of the kidneys, which showed a renal arteriovenous malformation pole on top of the left kidney.</p> <p>Conclusions</p> <p>The feeding artery of the arteriovenous malformation was selectively embolized with a microcatheter introduced using a right transfemoral approach. By using this technique, we stopped the bleeding, preserved renal parenchymal function, and relieved the patient's symptoms. The hemodynamic effects associated with the abnormality were also corrected.</p

Systemic Risk: Fire-Walling Financial Systems Using Network-Based Approaches

The latest financial crisis has painfully revealed the dangers arising from a globally interconnected financial system. Conventional approaches based on the notion of the existence of equilibrium and those which rely on statistical forecasting have seen to be inadequate to describe financial systems in any reasonable way. A more natural approach is to treat financial systems as complex networks of claims and obligations between various financial institutions present in an economy. The generic framework of complex networks has been successfully applied across several disciplines, e.g., explaining cascading failures in power transmission systems and epidemic spreading. Here we review various network models addressing financial contagion via direct inter-bank contracts and indirectly via overlapping portfolios of financial institutions. In particular, we discuss the implications of the "robust-yet-fragile" nature of financial networks for cost-effective regulation of systemic risk.Comment: 19 pages, 7 figure