Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and pressure for shifts acting on $X$ and obtain the existence of equilibrium states as additive probability measures for any bounded continuous potential. Furthermore, we establish convexity and other structural properties of the set of equilibrium states, prove a version of the Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity of the potential and show that the Yosida-Hewitt decomposition of these equilibrium states do not have a purely additive part. We then apply our results to the construction of invariant measures of time-homogeneous Markov chains taking values on a general Borel standard space and obtain exponential asymptotic stability for a class of Markov operators. We also construct conformal measures for an infinite collection of interacting random paths which are associated to a potential depending on infinitely many coordinates. Under an additional differentiability hypothesis, we show how this process is related after a proper scaling limit to a certain infinite dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical Systems. 23 page

Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces

We study a class of potentials $f$ on one sided full shift spaces over finite or countable alphabets, called potentials of product type. We obtain explicit formulae for the leading eigenvalue, the eigenfunction (which may be discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness property of these quantities is also discussed and it is shown that there always exists a Bernoulli equilibrium state even if $f$ does not satisfy Bowen's condition. We apply these results to potentials $f:\{-1,1\}^\mathbb{N} \to \mathbb{R}$ of the form $$f(x_1,x_2,\ldots) = x_1 + 2^{-\gamma} \, x_2 + 3^{-\gamma} \, x_3 + ...+n^{-\gamma} \, x_n + \ldots$$ with $\gamma >1$. For $3/2 < \gamma \leq 2$, we obtain the existence of two different eigenfunctions. Both functions are (locally) unbounded and exist a.s. (but not everywhere) with respect to the eigenmeasure and the measure of maximal entropy, respectively.Comment: To appear in the Journal of London Mathematical Societ

Differentiation and identification of White Riesling clones by genetic markers

Three different marker systems were used to genotype 10 clones of the grapevine cultivar White Riesling. All clones could be differentiated by means of genetic polymorphism gained by RAPD, SSR or Inter-SSR markers. While RAPD profile lacks stability for an identificational approach, individual SSR and Inter-SSR alleles could be retrieved within samples of the same clone. The polymorphic DNA fragments confirm the genetic variability within a traditional grapevine cultivar and the reproducibility of some of these markers allows the identification of clones. Since SSR and Inter-SSR markers show high stability when comparing data from different laboratories these methods are appropriate to establish data bases for the characterization of clonal grapevine material

Electro-catalytic Reduction of Aqueous Nitrates using Cu-Sn and Cu-Pd Cathodes

El articulo describe la remoción de nitratos y nitritos en agua para potabilización por un proceso electrocatalitico en escala laboratorio y pilotoWater treatment systems are used globally to reduce environmental impacts or to provide potable water, thus fulfilling established water quality standards. Electrocatalytic nitrate removal is a promising tool to address upcoming problems related to nitrate contamination. This study compares the employment of a low cost CuSn6 based catalyst with a noble metal Cu - Pd catalyst in a laboratory and a continuously operating pilot apparatus to treat nitrate contaminated water from a well. In contrast with common applications, a saturated carbonic acid was used as the anolyte solution, which stabilized the pH in the anode compartment as well as in the cathode compartment. The best performance, as determined by nitrate removal and nitrogen transfer into the gas phase, was reached with a specific current of 1.16 A m-2 for the laboratory apparatus and 1.53 A m-2 for the pilot plant apparatus. However, other parameters such as pH (influenced by anolyte solution) and catalyst selection also had an impact on the nitrate reduction performance with the consequence that process optimization should be realized on-site while running a pilot plant. Process gas analysis by mass spectroscopy revealed the presence of hydrogen, which suggests that a combination of the system with heterogeneous catalysts should be used for additional nitrogen reduction at potential free surfaces

Investigation of the chemical vicinity of crystal defects in ion-irradiated Mg and AZ31 with coincident Doppler broadening spectroscopy

Crystal defects in magnesium and magnesium based alloys like AZ31 are of major importance for the understanding of their macroscopic properties. We have investigated defects and their chemical surrounding in Mg and AZ31 on an atomic scale with Doppler broadening spectroscopy of the positron annihilation radiation. In these Doppler spectra the chemical information and the defect contribution have to be thoroughly separated. For this reason samples of annealed Mg were irradiated with Mg-ions in order to create exclusively defects. In addition Al- and Zn-ion irradiation on Mg-samples was performed in order to create samples with defects and impurity atoms. The ion irradiated area on the samples was investigated with laterally and depth resolved positron Doppler broadening spectroscopy (DBS) and compared with preceding SRIM-simulations of the vacancy distribution, which are in excellent agreement. The investigation of the chemical vicinity of crystal defects in AZ31 was performed with coincident Doppler broadening spectroscopy (CDBS) by comparing Mg-ion irradiated AZ31 with Mg-ion irradiated Mg. No formation of solute-vacancy complexes was found due to the ion irradiation, despite the high defect mobility.Comment: Submitted to Physical Review B on March 20 20076. Revised version submitted on September 28 2007. Accepted on October 19 200

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact

Patients with Acute Limb Ischemia Might Benefit from Endovascular Therapy—A 17-Year Retrospective Single-Center Series of 985 Patients

Acute lower limb ischemia (ALI) is a common vascular emergency, requiring urgent revascularization by open or endovascular means. The aim of this retrospective study was to evaluate patient demographics, treatment and periprocedural variables affecting the outcome in ALI patients in a consecutive cohort in a tertiary referral center. Primary outcome events (POE) were 30-day (safety) and 180-day (efficacy) combined mortality and major amputation rates, respectively. Secondary outcomes were perioperative medical and surgical leg-related complications and the 5-year combined mortality and major amputation rate. Statistical analysis used descriptive and uni- and multivariable Cox regression analysis. In 985 patients (71 ± 9 years, 56% men) from 2004 to 2020, the 30-day and 180-day combined mortality and major amputation rates were 15% and 27%. Upon multivariable analysis, older age (30 d: aHR 1.17; 180 d: 1.27) and advanced Rutherford ischemia stage significantly worsened the safety and efficacy POE (30 d: TASC IIa aHR 3.29, TASC IIb aHR 3.93, TASC III aHR 7.79; 180 d: TASC IIa aHR 1.97, TASC IIb aHR 2.43, TASC III aHR 4.2), while endovascular treatment was associated with significant improved POE after 30 days (aHR 0.35) and 180 days (aHR 0.39), respectively. Looking at five consecutive patient quintiles, a significant increase in endovascular procedures especially in the last quintile could be observed (17.5% to 39.5%, p < 0.001). Simultaneously, the re-occlusion rate as well as the number of patients with any previous revascularization increased. In conclusion, despite a slightly increasing early re-occlusion rate, endovascular treatment might, if possible, be favorable in ALI treatment

Extracorporeal liver assist device to exchange albumin and remove endotoxin in acute liver failure: Results of a pivotal pre-clinical study

Background & AimsIn acute liver failure, severity of liver injury and clinical progression of disease are in part consequent upon activation of the innate immune system. Endotoxaemia contributes to innate immune system activation and the detoxifying function of albumin, critical to recovery from liver injury, is irreversibly destroyed in acute liver failure. University College London-Liver Dialysis Device is a novel artificial extracorporeal liver assist device, which is used with albumin infusion, to achieve removal and replacement of dysfunctional albumin and reduction in endotoxaemia. We aimed to test the effect of this device on survival in a pig model of acetaminophen-induced acute liver failure.MethodsPigs were randomised to three groups: Acetaminophen plus University College London-Liver Dialysis Device (n=9); Acetaminophen plus Control Device (n=7); and Control plus Control Device (n=4). Device treatment was initiated two h after onset of irreversible acute liver failure.ResultsThe Liver Dialysis Device resulted in 67% reduced risk of death in acetaminophen-induced acute liver failure compared to Control Device (hazard ratio=0.33, p=0.0439). This was associated with 27% decrease in circulating irreversibly oxidised human non-mercaptalbumin-2 throughout treatment (p=0.046); 54% reduction in overall severity of endotoxaemia (p=0.024); delay in development of vasoplegia and acute lung injury; and delay in systemic activation of the TLR4 signalling pathway. Liver Dialysis Device-associated adverse clinical effects were not seen.ConclusionsThe survival benefit and lack of adverse effects would support clinical trials of University College London-Liver Dialysis Device in acute liver failure patients

Inorganic phosphate exporter heterozygosity in mice leads to brain vascular calcification, microangiopathy, and microgliosis

Calcification of the cerebral microvessels in the basal ganglia in the absence of systemic calcium and phosphate imbalance is a hallmark of primary familial brain calcification (PFBC), a rare neurodegenerative disorder. Mutation in genes encoding for sodium-dependent phosphate transporter 2 (SLC20A2), xenotropic and polytropic retrovirus receptor 1 (XPR1), platelet-derived growth factor B (PDGFB), platelet-derived growth factor receptor beta (PDGFRB), myogenesis regulating glycosidase (MYORG), and junctional adhesion molecule 2 (JAM2) are known to cause PFBC. Loss-of-function mutations in XPR1, the only known inorganic phosphate exporter in metazoans, causing dominantly inherited PFBC was first reported in 2015 but until now no studies in the brain have addressed whether loss of one functional allele leads to pathological alterations in mice, a commonly used organism to model human diseases. Here we show that mice heterozygous for Xpr1 (Xpr1$^{WT/lacZ}$ ) present with reduced inorganic phosphate levels in the cerebrospinal fluid and age- and sex-dependent growth of vascular calcifications in the thalamus. Vascular calcifications are surrounded by vascular basement membrane and are located at arterioles in the smooth muscle layer. Similar to previously characterized PFBC mouse models, vascular calcifications in Xpr1$^{WT/lacZ}$ mice contain bone matrix proteins and are surrounded by reactive astrocytes and microglia. However, microglial activation is not confined to calcified vessels but shows a widespread presence. In addition to vascular calcifications, we observed vessel tortuosity and transmission electron microscopy analysis revealed microangiopathy-endothelial swelling, phenotypic alterations in vascular smooth muscle cells, and thickening of the basement membrane