Urinary Calculi: Review of Classification Methods and Correlations with Etiology

Current physical and chemical methods available for urinary stones analysis are critically reviewed. No one method is sufficient to provide all the clinically useful information on the structure and composition of the stones. We show that a combination of refined morphological and structural examination of stone with optical microscopy, complemented by compositional analysis using infrared spectroscopy of the core, cross-section and surface of calculi, provides a precise and reliable method for identifying the structure and crystalline composition, and permits quantification of stone components while being highly cost effective. Using such morphoconstitutional studies leads to a classification of urinary stones in seven distinctive types and twenty-one subtypes among monohydrate (whewellite) and dihydrate (weddellite) calcium oxalates, phosphates, uric acid, urates, protein, and cystine calculi. Furthermore, all of the recognized sub-types exhibit correlations with specific pathophysiologic conditions. We conclude that such morphoconstitutional refined analysis and classification of urinary calculi is of interest to properly identify the type of stone disease and provides clues to etiopathogeny

On the Quality of First-Order Approximation of Functions with H\"older Continuous Gradient

We show that H\"older continuity of the gradient is not only a sufficient condition, but also a necessary condition for the existence of a global upper bound on the error of the first-order Taylor approximation. We also relate this global upper bound to the H\"older constant of the gradient. This relation is expressed as an interval, depending on the H\"older constant, in which the error of the first-order Taylor approximation is guaranteed to be. We show that, for the Lipschitz continuous case, the interval cannot be reduced. An application to the norms of quadratic forms is proposed, which allows us to derive a novel characterization of Euclidean norms

Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of graphs called path-complete graphs, and show that any such graph gives rise to a method for proving stability of the switched system. This enables us to derive several asymptotically tight hierarchies of semidefinite programming relaxations that unify and generalize many existing techniques such as common quadratic, common sum of squares, and maximum/minimum-of-quadratics Lyapunov functions. We compare the quality of approximation obtained by certain classes of path-complete graphs including a family of dual graphs and all path-complete graphs with two nodes on an alphabet of two matrices. We provide approximation guarantees for several families of path-complete graphs, such as the De Bruijn graphs, establishing as a byproduct a constructive converse Lyapunov theorem for maximum/minimum-of-quadratics Lyapunov functions.Comment: To appear in SIAM Journal on Control and Optimization. Version 2 has gone through two major rounds of revision. In particular, a section on the performance of our algorithm on application-motivated problems has been added and a more comprehensive literature review is presente

Methodological Aspects of Spontaneous Crystalluria Studies in Calcium Stone Formers

Despite nearly a half-century of study, the clinical value of spontaneous crystalluria (Cx) examinations in calcium stone formers (CaSF) is still uncertain. The analytical complexity of urine particle study is largely responsible for this situation. As a result, there is no consensus regarding technical methods in Cx with several techniques for urine sampling and three different instruments currently used for particle study, namely, particle counting (PC), light microscopy (LM) and petrographic microscopy (PM). In this work, we first examined urine sampling and instrument methods regarding their appropriateness for Cx studies. Then we performed a comparative analysis of Cx studies in CaSF. Despite many technical and clinical discrepancies, several studies agree that the frequency of all particles and of the weddellite and whewellite calcium oxalate (CaOx) crystalline phases are increased in CaSF as compared to normal subjects (NS). Particle sizes and aggregation ratio are also often increased. Altogether, these results reinforce the need for an efficient method for Cx studies in these patients. Examining each technique leads us to conclude that most particle parameters can be studied by direct LM observation of freshly voided urine samples, i.e., urine samples without any separation steps. For clinical applications, several examinations should be performed, first to define the specific Cx characteristics in a patient, then for the study of treatment efficiency on Cx control, and finally, during the patient follow-up. Due to Cx variability in each patient, the frequency of Cx examinations during each phase needs to be determined in long-term comparative prospective studies of CaSF

Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Double Exponential Instability of Triangular Arbitrage Systems

If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis to 5 or higher-order currency worlds. The key findings are that in a 5-currency world arbitrage sequences may also follow an exponential law as well as display periodicity, but that in higher-order currency worlds a double exponential law may additionally apply. There is an "inheritance of instability" in the higher-order currency worlds. Profitable arbitrage operations are thus endemic rather that displaying the self-extinguishing properties implied by the EMH.Comment: 22 pages, 22 bibliography references, expanded Introduction and Conclusion, added bibliohraphy reference

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

r.hu-Erythropoietin (EPO) treatment of pre-ESRD patients slows the rate of progression of renal decline

BACKGROUND: As EPO treatment of chronic anemia of advanced renal disease is now the standard of care we examined if such treatment may slow the progression of renal function decline. METHODS: Data of 18 pre-ESRD patients were analyzed retrospectively 12 months prior and prospectively 12 months after the initiation of EPO. Mean creatinine was 5.0 ± 1.8 mg/dL (Mean ± SEM) when starting EPO at a weekly dose of 5000 ± 500 units once the hematocrit was below 30 %. EPO dose was titrated monthly for a hematocrit between 33.0% and 37.0%. Metabolic complications and hypertension were controlled. RESULTS: At month_0 the average blood pressure was 148/76 ± 5/4 mmHg and at month_12 it was 145/73 ± 6/3 mmHg (p = 0.75 by 2 tailed paired Student's t test). 12/18 patients were on an ACE-i or ARB before month_0 and 14/18 were on it after (p = 0.71 by Fisher's 2 tailed exact test). The average hematocrit rose from 26.9% ± 0.6 to 33.1 % ± 0.1. When linear regression analysis was applied to pre- and post-EPO 1/creatinine data the mean rate of decline was -0.0140 ± 0.0119 (mean ± SD) and -0.0017 ± 0.0090 (non-parametric Wilcoxon matched pairs signed rank sum test: Z value: -2.91; P = 0.004) respectively. 5/18 patients did not require dialysis 12 months after starting EPO (month_0). CONCLUSION: Treatment of the anemia of chronic renal failure with erythropoietin, when instituted together with vigorous metabolic control may slow the rate of renal function decline