Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

Is there an age cutoff to apply adult formulas for GFR estimation in children?

BACKGROUND Estimation of glomerular filtration rate (eGFR) using a common formula for both adult and pediatric populations is challenging. Using inulin clearances (iGFRs), this study aims to investigate the existence of a precise age cutoff beyond which the Modification of Diet in Renal Disease (MDRD), the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI), or the Cockroft-Gault (CG) formulas, can be applied with acceptable precision. Performance of the new Schwartz formula according to age is also evaluated. METHOD We compared 503 iGFRs for 503 children aged between 33 months and 18 years to eGFRs. To define the most precise age cutoff value for each formula, a circular binary segmentation method analyzing the formulas' bias values according to the children's ages was performed. Bias was defined by the difference between iGFRs and eGFRs. To validate the identified cutoff, 30% accuracy was calculated. RESULTS For MDRD, CKD-EPI and CG, the best age cutoff was ≥14.3, ≥14.2 and ≤10.8 years, respectively. The lowest mean bias and highest accuracy were -17.11 and 64.7% for MDRD, 27.4 and 51% for CKD-EPI, and 8.31 and 77.2% for CG. The Schwartz formula showed the best performance below the age of 10.9 years. CONCLUSION For the MDRD and CKD-EPI formulas, the mean bias values decreased with increasing child age and these formulas were more accurate beyond an age cutoff of 14.3 and 14.2 years, respectively. For the CG and Schwartz formulas, the lowest mean bias values and the best accuracies were below an age cutoff of 10.8 and 10.9 years, respectively. Nevertheless, the accuracies of the formulas were still below the National Kidney Foundation Kidney Disease Outcomes Quality Initiative target to be validated in these age groups and, therefore, none of these formulas can be used to estimate GFR in children and adolescent populations.

Sampling associated with resolvent-type kernels and lagrange-type interpolation series

In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associ- ated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.

Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds for arbitrary atomic numbers and fine structure constant. We also announce bounds for the energy of many electrons and nuclei in a classical vector potential and for the eigenvalue sum of a one-electron Pauli Hamiltonian with magnetic field.

Mutations of γ-aminobutyric acid and glycine receptors change alcohol cutoff: Evidence for an alcohol receptor?

Alcohols in the homologous series of n-alcohols increase in central nervous system depressant potency with increasing chain length until a “cutoff” is reached, after which further increases in molecular size no longer increase alcohol potency. A similar phenomenon has been observed in the regulation of ligand-gated ion channels by alcohols. Different ligand-gated ion channels exhibit radically different cutoff points, suggesting the existence of discrete alcohol binding pockets of variable size on these membrane proteins. The identification of amino acid residues that determine the alcohol cutoff may, therefore, provide information about the location of alcohol binding sites. Alcohol regulation of the glycine receptor is critically dependent on specific amino acid residues in transmembrane domains 2 and 3 of the α subunit. We now demonstrate that these residues in the glycine α1 and the γ-aminobutyric acid ρ1 receptors also control alcohol cutoff. By mutation of Ser-267 to Gln, it was possible to decrease the cutoff in the glycine α1 receptor, whereas mutation of Ile-307 and/or Trp-328 in the γ-aminobutyric acid ρ1 receptor to smaller residues increased the cutoff. These results support the existence of alcohol binding pockets in these membrane proteins and suggest that the amino acid residues present at these positions can control the size of the alcohol binding cavity.

The cutoff phenomenon in finite Markov chains.

Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists.

Diagnosis of diabetes mellitus: case of different cutoff values: A data mining approach

Objective: An estimation of cut-off points for the diagnosis of diabetes mellitus (DM) based on individual risk factors. Methods: A subset of the 1991 Oman National Diabetes Survey is used, including all patients with a 2h post glucose load >= 200 mg/dl (278 subjects) and a control group of 286 subjects. All subjects previously diagnosed as diabetic and all subjects with missing data values were excluded. The data set was analyzed by use of the SPSS Clementine data mining system. Decision Tree Learners (C5 and CART) and a method for mining association rules (the GRI algorithm) are used. The fasting plasma glucose (FPG), age, sex, family history of diabetes and body mass index (BMI) are input risk factors (independent variables), while diabetes onset (the 2h post glucose load >= 200 mg/dl) is the output (dependent variable). All three techniques used were tested by use of crossvalidation (89.8%). Results: Rules produced for diabetes diagnosis are: A- GRI algorithm (1) FPG>=108.9 mg/dl, (2) FPG>=107.1 and age>39.5 years. B- CART decision trees: FPG >=110.7 mg/dl. C- The C5 decision tree learner: (1) FPG>=95.5 and 54, (2) FPG>=106 and 25.2 kg/m2. (3) FPG>=106 and =133 mg/dl. The three techniques produced rules which cover a significant number of cases (82%), with confidence between 74 and 100%. Conclusion: Our approach supports the suggestion that the present cut-off value of fasting plasma glucose (126 mg/dl) for the diagnosis of diabetes mellitus needs revision, and the individual risk factors such as age and BMI should be considered in defining the new cut-off value.

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

Protein cutoff scanning: a comparative analysis of cutoff dependent and cutoff free methods for prospecting contacts in proteins.

In this study, we carried out a comparative analysis between two classical methodologies to prospect residue contacts in proteins: the traditional cutoff dependent (CD) approach and cutoff free Delaunay tessellation (DT). In addition, two alternative coarse-grained forms to represent residues were tested: using alpha carbon (CA) and side chain geometric center (GC). A database was built, comprising three top classes: all alpha, all beta, and alpha/beta. We found that the cutoff value? at about 7.0 A emerges as an important distance parameter.? Up to 7.0 A, CD and DT properties are unified, which implies that at this distance all contacts are complete and legitimate (not occluded). We also have shown that DT has an intrinsic missing edges problem when mapping the first layer of neighbors. In proteins, it may produce systematic errors affecting mainly the contact network in beta chains with CA. The almost-Delaunay (AD) approach has been proposed to solve this DT problem. We found that even AD may not be an advantageous solution. As a consequence, in the strict range up ? to 7.0 A, the CD approach revealed to be a simpler, more complete, and reliable technique than DT or AD. Finally, we have shown that coarse-grained residue representations may introduce bias in the analysis of neighbors in cutoffs up to ? 6.8 A, with CA favoring alpha proteins and GC favoring beta proteins. This provides an additional argument pointing to ? the value of 7.0 A as an important lower bound cutoff to be used in contact analysis of proteins.

The correlation of pore morphology, interconnectivity and physical properties of 3D ceramic scaffolds with bone ingrowth

In the design of tissue engineering scaffolds, design parameters including pore size, shape and interconnectivity, mechanical properties and transport properties should be optimized to maximize successful inducement of bone ingrowth. In this paper we describe a 3D micro-CT and pore partitioning study to derive pore scale parameters including pore radius distribution, accessible radius, throat radius, and connectivity over the pore space of the tissue engineered constructs. These pore scale descriptors are correlated to bone ingrowth into the scaffolds. Quantitative and visual comparisons show a strong correlation between the local accessible pore radius and bone ingrowth; for well connected samples a cutoff accessible pore radius of approximately 100 microM is observed for ingrowth. The elastic properties of different types of scaffolds are simulated and can be described by standard cellular solids theory: (E/E(0))=(rho/rho(s))(n). Hydraulic conductance and diffusive properties are calculated; results are consistent with the concept of a threshold conductance for bone ingrowth. Simple simulations of local flow velocity and local shear stress show no correlation to in vivo bone ingrowth patterns. These results demonstrate a potential for 3D imaging and analysis to define relevant pore scale morphological and physical properties within scaffolds and to provide evidence for correlations between pore scale descriptors, physical properties and bone ingrowth.

An examination of the utility of the AUDIT in people with schizophrenia

Objective: To examine the reliability and validity of the Alcohol Use Disorders Identification Test (AUDIT) compared to a structured diagnostic interview, the Composite international Diagnostic Interview (CIDI; 12-month version) in psychiatric patients with a diagnosis of schizophrenia. Method: Patients (N = 71, 53 men) were interviewed using the CIDI (Alcohol Misuse Section; 12-month version) and then completed the AUDIT. Results: The CIDI identified 32.4% of the sample as having an alcohol use disorder. Of these, 5 (7.0%) met diagnostic criteria for harmful use of alcohol, 1 (1.4%) met diagnostic criteria for alcohol abuse and 17 (23.9%) met diagnostic criteria for alcohol dependence. The AUDIT was found to have good internal reliability (coefficient = 0.85). An AUDIT cutoff of greater than or equal to 8 had a sensitivity of 87% and specificity of 90% in detecting CIDI-diagnosed alcohol disorders. All items except Item 9 contributed significantly to discriminant validity. Conclusions: The findings replicate and extend previous findings of high rates of alcohol use disorders in people with severe mental illness. The AUDIT was found to be reliable and valid in this sample and can be used with confidence as a screening instrument for alcohol use disorders in people with schizophrenia.

Development and validation of 3-Minute Nutrition Screening (3-MinNS) tool for acute hospital patients in Singapore

It is important to detect and treat malnutrition in hospital patients so as to improve clinical outcome and reduce hospital stay. The aim of this study was to develop and validate a nutrition screening tool with a simple and quick scoring system for acute hospital patients in Singapore. In this study, 818 newly admitted patients aged above 18 years old were screened using five parameters that contribute to the risk of malnutrition. A dietitian blinded to the nutrition screening score assessed the same patients using the reference standard, Subjective Global Assessment (SGA) within 48 hours. The sensitivity and specificity were established using the Receiver Operator Characteristics (ROC) curve and the best cutoff scores determined. The nutrition parameter with the largest Area Under the ROC Curve (AUC) was chosen as the final screening tool, which was named 3-Minute Nutrition Screening (3-MinNS). The combination of the parameters weight loss, intake and muscle wastage (3-MinNS), gave the largest AUC when compared with SGA. Using 3-MinNS, the best cutoff point to identify malnourished patients is three (sensitivity 86%, specificity 83%). The cutoff score to identify subjects at risk of severe malnutrition is five (sensitivity 93%, specificity 86%). 3-Minute Nutrition Screening is a valid, simple and rapid tool to identify patients at risk of malnutrition in Singapore acute hospital patients. It is able to differentiate patients at risk of moderate malnutrition and severe malnutrition for prioritization and management purposes.

Corneal confocal microscopy : a novel noninvasive test to diagnose and stratify the severity of human diabetic neuropathy

OBJECTIVE: The accurate quantification of human diabetic neuropathy is important to define at-risk patients, anticipate deterioration, and assess new therapies. ---------- RESEARCH DESIGN AND METHODS: A total of 101 diabetic patients and 17 age-matched control subjects underwent neurological evaluation, neurophysiology tests, quantitative sensory testing, and evaluation of corneal sensation and corneal nerve morphology using corneal confocal microscopy (CCM). ---------- RESULTS: Corneal sensation decreased significantly (P = 0.0001) with increasing neuropathic severity and correlated with the neuropathy disability score (NDS) (r = 0.441, P < 0.0001). Corneal nerve fiber density (NFD) (P < 0.0001), nerve fiber length (NFL), (P < 0.0001), and nerve branch density (NBD) (P < 0.0001) decreased significantly with increasing neuropathic severity and correlated with NDS (NFD r = −0.475, P < 0.0001; NBD r = −0.511, P < 0.0001; and NFL r = −0.581, P < 0.0001). NBD and NFL demonstrated a significant and progressive reduction with worsening heat pain thresholds (P = 0.01). Receiver operating characteristic curve analysis for the diagnosis of neuropathy (NDS >3) defined an NFD of <27.8/mm2 with a sensitivity of 0.82 (95% CI 0.68–0.92) and specificity of 0.52 (0.40–0.64) and for detecting patients at risk of foot ulceration (NDS >6) defined a NFD cutoff of <20.8/mm2 with a sensitivity of 0.71 (0.42–0.92) and specificity of 0.64 (0.54–0.74). ---------- CONCLUSIONS: CCM is a noninvasive clinical technique that may be used to detect early nerve damage and stratify diabetic patients with increasing neuropathic severity. Established diabetic neuropathy leads to pain and foot ulceration. Detecting neuropathy early may allow intervention with treatments to slow or reverse this condition (1). Recent studies suggested that small unmyelinated C-fibers are damaged early in diabetic neuropathy (2–4) but can only be detected using invasive procedures such as sural nerve biopsy (4,5) or skin-punch biopsy (6–8). Our studies have shown that corneal confocal microscopy (CCM) can identify early small nerve fiber damage and accurately quantify the severity of diabetic neuropathy (9–11). We have also shown that CCM relates to intraepidermal nerve fiber loss (12) and a reduction in corneal sensitivity (13) and detects early nerve fiber regeneration after pancreas transplantation (14). Recently we have also shown that CCM detects nerve fiber damage in patients with Fabry disease (15) and idiopathic small fiber neuropathy (16) when results of electrophysiology tests and quantitative sensory testing (QST) are normal. In this study we assessed corneal sensitivity and corneal nerve morphology using CCM in diabetic patients stratified for the severity of diabetic neuropathy using neurological evaluation, electrophysiology tests, and QST. This enabled us to compare CCM and corneal esthesiometry with established tests of diabetic neuropathy and define their sensitivity and specificity to detect diabetic patients with early neuropathy and those at risk of foot ulceration.

Corneal sensitivity as an ophthalmic marker of diabetic neuropathy

Purpose. The objective of this study was to explore the discriminative capacity of non-contact corneal esthesiometry (NCCE) when compared with the neuropathy disability score (NDS) score—a validated, standard method of diagnosing clinically significant diabetic neuropathy. Methods. Eighty-one participants with type 2 diabetes, no history of ocular disease, trauma, or surgery and no history of systemic disease that may affect the cornea were enrolled. Participants were ineligible if there was history of neuropathy due to non-diabetic cause or current diabetic foot ulcer or infection. Corneal sensitivity threshold was measured on the eye of dominant hand side at a distance of 10 mm from the center of the cornea using a stimulus duration of 0.9 s. The NDS was measured producing a score ranging from 0 to 10. To determine the optimal cutoff point of corneal sensitivity that identified the presence of neuropathy (diagnosed by NDS), the Youden index and “closest-to-(0,1)” criteria were used. Results. The receiver-operator characteristic curve for NCCE for the presence of neuropathy (NDS ≥3) had an area under the curve of 0.73 (p = 0.001) and, for the presence of moderate neuropathy (NDS ≥6), area of 0.71 (p = 0.003). By using the Youden index, for an NDS ≥3, the sensitivity of NCCE was 70% and specificity was 75%, and a corneal sensitivity threshold of 0.66 mbar or higher indicated the presence of neuropathy. When NDS ≥6 (indicating risk of foot ulceration) was applied, the sensitivity was 52% with a specificity of 85%. Conclusions. NCCE is a sensitive test for the diagnosis of minimal and more advanced diabetic neuropathy and may serve as a useful surrogate marker for diabetic and perhaps other neuropathies.