Number Of Critical Values Research Articles

Optimal state discrimination with an error margin of pure and mixed symmetric states: irreducible qudit and reducible qubit states

Minimum error discrimination (MED) and Unambiguous discrimination (UD) are two common strategies for quantum state discrimination that can be modified by imposing a finite error margin on the error probability. Error margins 0 and 1 correspond to two common strategies. In this paper, for an arbitrary error margin m, the discrimination problem of equiprobable quantum symmetric states is analytically solved for four distinct cases. A generating set of irreducible and reducible representations of a subgroup of a unitary group are considered, separately, as unitary operators that produce one set of the symmetric states. In the irreducible case, for mixed and pure qudit states, one critical m which divides the parameter space into two domains is obtained. The number of critical values m in the reducible case is two, for both N mixed and pure qubit states. The reason for this difference between numbers of critical values m is explained. The optimal set of measurements and corresponding maximum success probability in fully analytical form are determined for all values of the error margin. The relationship between the amount of error that is imposed on error probability and geometrical situation of states with changes in rank of element corresponding to inconclusive result is determined. The behaviors of elements of measurement are explained geometrically in order to decrease the error probability in each domain. Furthermore, the problem of the discrimination with error margin among elements of two different sets of symmetric quantum states is studied. The number of critical values m is equivalent to one set in both reducible and irreducible cases. In addition, optimal measurements in each domain are obtained.

Analysis of Laboratory Critical value Reporting Pattern at clinical biochemistry laboratory of Tertiary health care Center

Objectives: Objective of the study is to analyze critical value reporting data to find frequency of critical reporting, distribution of critical values across reportable range and across hospital segments and reasons for failure in critical reporting. Material & Method: The critical value reporting data for various analysts were collected from LIS for 1 year. The data were analyzed in computer spreadsheets. Result & Discussion: Of 548786 test results analyzed, about 10% results were critical. Total Billirubin (20.14 %), Indirect Billirubin (18 %), Glucose (18%) and Sodium (13.6 %),Potassium (11.8%) contributed most to the critical values. 29% of urea, 13.29 % of Glucose ,15.37% of Indirect Billirubin, 13.71% of Sodium, 13.29% of Glucose & 11.6 % of total analyzed potassium were critical. On a per test basis, inpatient tests were 3.6 times more likely to result in a critical callback than outpatient tests. The number of critical values per year per bed was 176.34 for ICU beds and 29.36 for non-ICU beds and 5.0 for Emergency Department. Conclusion: The high proportion of reported critical value of urea is due to practice of reflex testing in the laboratory whenever Creatinine is in abnormal range. The high proportion of reported critical value of Indirect Billirubin is due to present of PICU, NICU in Hospital. Major reasons for failure of notification of critical alert are incomplete detail on request form, transfer of patient to Ward or ICU, phone is engaged or phone not picked up by care giver.

Should we customise critical value procedure according to patient origin and laboratory turnaround time?

IntroductionOur routine laboratory critical value notification procedure is based on a short list of six fundamental critical values. The report system for our Stat laboratory is not based on this...

Constant weighted sums of iterates

We define and study when a polynomial mapping has a constant weighted sum of iterates, either locally or globally. We conjecture that a polynomial f in the complex plane has a constant weighted sum of iterates near a point z if and only if z is eventually mapped into a Siegel-disc of f. We prove that this conjecture holds generically, namely for those polynomials whose iterates have the maximal number of critical values. Important steps in the proofs rely on understanding the monodromy groups of the iterates of f. We also show that a polynomial automorphism of ℂ2 has a global constant weighted sum of iterates if and only if the map is conjugate to an elementary mapping. The definition of a constant weighted sum of iterates is motivated by an attempt to understand the polynomial automorphism groups in dimensions 3 and higher.

Retrospective Study of Critical Values: Agreement and Improvement

Background: Accreditation agencies now require clinical laboratories to list critical limits, formulate notification procedures, document critical results, and notify clinicians. The objective of this study has been to perform a retrospective review of our critical value notification procedure and improve it by reaching a consensus with our clinicians. Methods: The main outcome measures were the number of critical values (CVs) reported in our laboratory and the number and rate of CVs if we had applied the universal critical limit list used by the majority and the supercritical limit list. Results: Fifty-four CVs were reported with 660 theoretical CVs and 120 supercritical CVs. The list CV and notification procedure was improved according to expert opinion. Conclusion: Every laboratory should have at its disposal a procedure to notify critical results. A consensus should be reached with clinicians to establish a specific list of critical limits according to the type of patient and the timeliness of laboratory tests.

Calculation of Critical Values for Somerville's FDR Procedures

A Fortran 95 program has been written to calculate critical values for the step-up and step-down FDR procedures developed by Somerville (2004). The program allows for arbitrary selection of number of hypotheses, FDR rate, one- or two-sided hypotheses, common correlation coefficient of the test statistics and degrees of freedom. An MCV (minimum critical value) may be specified, or the program will calculate a specified number of critical values or steps in an FDR procedure. The program can also be used to efficiently ascertain an upper bound to the number of hypotheses which the procedure will reject, given either the values of the test statistics, or their p values. Limiting the number of steps in an FDR procedure can be used to control the number or proportion of false discoveries (Somerville and Hemmelmann 2007). Using the program to calculate the largest critical values makes possible efficient use of the FDR procedures for very large numbers of hypotheses.

Invariance of Milnor numbers and topology of complex polynomials

We give a global version of Le-Ramanujam μ-constant theorem for polynomials. Let \((f_t)\), \(t\in[0,1]\), be a family of polynomials of n complex variables with isolated singularities, whose coefficients are polynomials in t. We consider the case where some numerical invariants are constant (the affine Milnor number μ(t), the Milnor number at infinity λ(t), the number of critical values, the number of affine critical values, the number of critical values at infinity). Let n=2, we also suppose the degree of the \(f_t\) is a constant, then the polynomials \(f_0\) and \(f_1\) are topologically equivalent. For \(n>3\) we suppose that critical values at infinity depend continuously on t, then we prove that the geometric monodromy representations of the \(f_t\) are all equivalent.

Regional inference with averaged P values increases the power to detect linkage.

Controversy exists with respect to the choice of an appropriate critical value when testing for linkage in a genomic screen. A number of critical values have been proposed for single-locus and multi-locus linkage analyses. In this study, criteria based on multiple single-locus analyses (i.e., regional test criteria) are evaluated using simulation methods for three different map densities. Tests based on single loci, multiple consecutive single loci, and moving averages of consecutive single loci are considered. Appropriate critical values are determined based on results from simulations under the null hypothesis of no linkage. The power of each "regional test " was compared to the power of a single-locus test. Results suggest that the best power was found when averaging P values over an interval size of 9-15 cM, and that testing the average of P values from two consecutive loci is superior to testing each single locus separately. The increase in power ranged from 7- 29% over the simulations considered.

Estimation of the Number of the Critical Values at Infinity of a Polynomial Function $f:\mathbf C^2 → \mathbf C$

is not necessarily a locally trivial fibration. In general, we have to exclude a finite values Z^ c C from the base space so that / : C f~ (L u Z^ ) — > C (Z u Z^ ) is a locally trivial fibration. We say that r e C is a regular value at infinity of the function / : C — > C if there exist positive numbers R and 8 so that the restriction of/, f:f-(D£(T))-B*^>D£(T),is a trivial fibration over the disc D£(r) where De(T) = {r]£C\\ri-i\<£} and B*=[(x,y);x 2 =\y <R}. Otherwise ris a called a critical value at infinity or an atypical value. We denote the set of the critical values at infinity by Z^. It is known that Z^ is finite ([V], [HI]). This fact also results from Theorem (1.4). The purpose of this note is to give an estimation on the number of critical values at infinity.

Singularities admitting perturbations with a small number of critical values

Singularities admitting perturbations with a small number of critical values