The Higher Order Schwarzian Derivative: Its Applications for Chaotic Behavior and New Invariant Sufficient Condition of Chaos

The Schwarzian derivative of a function f(x) which is defined in the interval (a, b) having higher order derivatives is given by Sf(x)=(f''(x)/f'(x))'-1/2(f''(x)/f'(x))^2 . A sufficient condition for a function to behave chaotically is that its Schwarzian derivative is negative. In this paper, we try to find a sufficient condition for a non-linear dynamical system to behave chaotically. The solution function of this system is a higher degree polynomial. We define n-th Schwarzian derivative to examine its general properties. Our analysis shows that the sufficient condition for chaotic behavior of higher order polynomial is provided if its highest order three terms satisfy an inequality which is invariant under the degree of the polynomial and the condition is represented by Hankel determinant of order 2. Also the n-th order polynomial can be considered to be the partial sum of real variable analytic function. Let this analytic function be the solution of non-linear differential equation, then the sufficient condition for the chaotical behavior of this function is the Hankel determinant of order 2 negative, where the elements of this determinant are the coefficient of the terms of n, n-1, n-2 in Taylor expansion.Comment: 8 page

Surface activated chemical ionization - Electrospray mass spectrometry in the analysis of urinary thiodiglycolic acid

RATIONALE Thiodiglycolic acid (TDGA) is a urinary metabolite of the oxazaphosphorine class of chemotherapeutics, in particular of ifosfamide. Ifosfamide metabolism generates chloroacetaldehyde (CAA), a toxic compound associated with neurotoxicity, nephrotoxicity, urotoxicity and cardiotoxicity. CAA, in turn, interacts with cellular thiol groups leading to GSH depletion, cell death and generation of thiodiglycolic acid (TDGA), as a final product. TDGA is mainly excreted in the urine. The ability to accurately measure TDGA in urine, therefore, will be a useful way of monitoring the ifosfamide exposure during chemotherapy. METHODS TDGA in urine samples was measured with liquid chromatograpy coupled to mass spectrometry (LC-MS) by means of a novel Surface Activated Chemical Ionization - Electrospray (SACI-ESI) or a classical ESI ion source alone. RESULTS The SACI - ESI and ESI alone based methods for analysis of urinary TDGA were optimized and compared. A strong reduction in matrix effect together with enhanced quantification performances was obtained with the SACI \u2013 ESI when compared with the ESI. In particular, an increase in quantification precision (from 85 to 95%) and accuracy (from 59 to 90%) were observed, which allowed for optimal detection of TDGA. CONCLUSIONS The LC-SACI-ESI-MS approach provides a very sensitive and quantitative method for the analysis of TDGA. Thanks to sensitivity enhancement and matrix effect reduction, the SACI \u2013 ESI enables the use of a relatively low cost ion-trap mass spectrometer in the analysis of this toxicity biomarker in urine. Due to these characteristics, this approach would constitutes an invaluable tool in the clinical laboratory, for measuring TDGA and other toxicity related biomarkers of chemotherapy with proper sensitivity and accuracy

Sustained inflammation 1.5 years post-stroke is not associated with depression in elderly stroke survivors

Background: Depression is common in elderly stroke survivors and has been associated with systemic inflammation. We aimed to investigate an elderly population of Swedish stroke patients for evidence of sustained peripheral inflammation 18 months post-stroke and to identify if inflammation is associated with post-stroke depression at 18 months post-stroke. Methods: The Barthel Index was used to measure the level of impairment in activities of daily living at 3 days post-stroke. Serum concentrations of inflammation markers, ie, C-reactive protein and white cell count, were measured in 149 stroke patients (mean age 81 ± 5.33 years, 35% male) at 18 months post-stroke, and a comparison was made with an age-matched sample of elderly Swedish individuals who had not suffered a stroke. At the same visit, clinical depression was diagnosed according to the Diagnostic and Statistical Manual of Mental Disorders, Third Edition-Revised criteria. Severity of depression was assessed using the Montgomery-Asberg Depression Rating Scale (MADRS). Results: Mean C-reactive protein and white cell count levels in stroke patients were significantly elevated at 18 months post-stroke compared with population probands. Disability scores were associated with MADRS depression scores, but C-reactive protein and white cell count were not. Conclusion: We found evidence for a sustained peripheral inflammatory response at 18 months post-stroke. C-reactive protein and white cell count were not associated with depression in this study

RNASET2 as a tumor antagonizing gene in a melanoma cancer model

The RNASET2 gene, mapped in 6q27, was previously found to exert control of tumorigenesis in an ovarian cancer system. We present here results indicating a similar control in a melanoma cancer model. Thus, this gene is most likely involved in a common general pathway of tumorigenesis. Moreover, its antitumorigenic activity is manifested in vivo but not in vitro, suggesting that this gene belongs to the growing category of tumor antagonizing/malignancy suppressor genes. A possible role of RNASET2 in the activation of a senescence program, whose responsible locus was mapped in the same chromosomal 6q27 region, seems to be inconsistent with our data

A Polyphenol-Rich Extract of Olive Mill Wastewater Enhances Cancer Chemotherapy Effects, While Mitigating Cardiac Toxicity

Cardiovascular toxicity remains one of the most adverse side effects in cancer patients receiving chemotherapy. Extra-virgin olive oil (EVOO) is rich in cancer preventive polyphenols endowed with anti-inflammatory, anti-oxidant activities which could exert protective effects on heart cells. One very interesting derivative of EVOO preparation is represented by purified extracts from olive mill waste waters (OMWW) rich in polyphenols. Here, we have investigated the anti-cancer activity of a OMWW preparation, named A009, when combined with chemotherapeutics, as well as its potential cardioprotective activities. Mice bearing prostate cancer (PCa) xenografts were treated with cisplatin, alone or in combination with A009. In an in vivo model, we found synergisms of A009 and cisplatin in reduction of prostate cancer tumor weight. Hearts of mice were analyzed, and the mitochondria were studied by transmission electron microscopy. The hearts of mice co-treated with A009 extracts along with cisplatin had reduced mitochondria damage compared to the those treated with chemotherapy alone, indicating a cardioprotective role. To confirm the in vivo results, tumor cell lines and rat cardiomyocytes were treated with cisplatin in vitro, with and without A009. Another frequently used chemotherapeutic agent 5-fluorouracil (5-FU), was also tested in this assay, observing a similar effect. In vitro, the combination of A009 with cisplatin or 5-FU was effective in decreasing prostate and colon cancer cell growth, while it did not further reduce growth of rat cardiomyocytes also treated with cisplatin or 5-FU. A009 cardioprotective effects towards side effects caused by 5-FU chemotherapy were further investigated, using cardiomyocytes freshly isolated from mice pups. A009 mitigated toxicity of 5-FU on primary cultures of mouse cardiomyocytes. Our study demonstrates that the polyphenol rich purified A009 extracts enhance the effect of chemotherapy in vitro and in vivo, but mitigates chemotherpy adverse effects on heart and on isolated cardiomyocytes. Olive mill waste water extracts could therefore represent a potential candidate for cardiovascular prevention in patients undergoing cancer chemotherapy

Scaling of Self-Avoiding Walks in High Dimensions

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to $1/d$-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, $\mu_5=8.838544(3)$, $\mu_6=10.878094(4)$, $\mu_7=12.902817(3)$, $\mu_8=14.919257(2)$ and give a revised estimate of $\mu_4=6.774043(5)$. All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in $d>4$ and all approaches in $d=4$). Our results are consistent with most theoretical predictions, though in $d=5$ we find clear evidence of anomalous $N^{-1/2}$-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form $N^{(4-d)/2}$ (not present in pure Gaussian random walks).Comment: 14 pages, 2 figure

A Characterisation of Strong Wave Tails in Curved Space-Times

A characterisation of when wave tails are strong is proposed. The existence of a curvature induced tail (i.e. a Green's function term whose support includes the interior of the light-cone) is commonly understood to cause backscattering of the field governed by the relevant wave equation. Strong tails are characterised as those for which the purely radiative part of the field is backscattered. With this definition, it is shown that electromagnetic waves in asymptotically flat space-times and fields governed by tail-free propagation have weak tails, but minimally coupled scalar fields in a cosmological scenario have strong tails.Comment: 17 pages, Revtex, to appear in Classical and Quantum Gravit

Complete Experimental Structure Determination of the p(3x2)pg Phase of Glycine on Cu{110}

We present a quantitative low energy electron diffraction (LEED) surface-crystallograpic study of the complete adsorption geometry of glycine adsorbed on Cu{110} in the ordered p(3×2) phase. The glycine molecules form bonds to the surface through the N atoms of the amino group and the two O atoms of the de-protonated carboxylate group, each with separate Cu atoms such that every Cu atom in the first layer is involved in a bond. Laterally, N atoms are nearest to the atop site (displacement 0.41 Å). The O atoms are asymmetrically displaced from the atop site by 0.54 Å and 1.18 Å with two very different O-Cu bond lengths of 1.93 Å and 2.18 Å. The atom positions of the upper-most Cu layers show small relaxations within 0.07 Å of the bulk-truncated surface geometry. The unit cell of the adsorbate layer consists of two glycine molecules, which are related by a glide-line symmetry operation. This study clearly shows that a significant coverage of adsorbate structures without this glide-line symmetry must be rejected, both on the grounds of the energy dependence of the spot intensities (LEED-IV curves) and of systematic absences in the LEED pattern