LetX1,X2, . . . ,Xk be independent n bit random variables. If they have arbitrary distributions, we show how to compute distributions like Pr{X1 ⊕X2 ⊕ · · · ⊕Xk} and Pr{X1 X2 · · · Xk} in complexity O(kn2). Furthermore, if X1,X2, . . . , Xk are uniformly distributed we demonstrate a large class of functions F (X1, X2, . . . ,Xk), for which we can compute their distributions efficiently. These r...

(In first case we say (F,G2) are an adjoint pair and in the second case we say that (G1, F ) are an adjoint pair.) (2) An object A in a category C is called initial (resp. final) if for every object B in C, HomC(A,B) (resp. HomC(B,A)) is a singleton. Prove that an initial (resp. final) object, if it exists, is unique up to unique isomorphism. Determine if such objects exist in the following cat...

Let consider a sample of n individuals with nc controls and nd cases (nc+nd = n) and Y = [y1, . . . , yn] ′ the vector of the observed binary phenotypes. Each gene is a collection of respectively m1 and m2 SNPs. The observed genotypes for gene X1 can be represented by a n×m1 matrix: X1 = [xij ]i∈1...n;j∈1...m1 where xij ∈ {0; 1; 2} is the number of copies of the minor allele for SNP j carried b...


 Current study aimed to explore the prevalence of dental problems including caries among 12 years old students studying in public and private sector schools Pakistan. 677 were recruited from 2 Lahore. Significant difference between was found terms (X2= 35.094, P<.001). scaling requirement X2=54.778, gum bleeding (X2=35.245, not Plaque accumulation (X2=54.778, fluorosis (X2=44.557, In c...

Background : Though POSSUM and P-POSSUM have been proposed as accurate tools of audit, our initial experience has not been encouraging. Therefore, a prospective study was conducted to find their accuracy for predicting outcome in peritonitis patients who underwent emergency laparotomy. Methods : 172 patients treated in single surgical unit over two years were included. Expected morbidity and mo...

هدف: هدف از انجام این پژوهش مقایسه اثربخشی طرح‌واره‌درمانی و واقعیت‌درمانی بر انعطاف‌پذیری روان‌شناختی خودتنظیمی هیجانی مربیان پیش‌دبستانی شهرستان شهرکرد بود. روش: جامعه آماری کلیة شهرکردبودند که بین آنها تعداد 45 نفر به صورت نمونه‌گیری در دسترس انتخاب گمارش تصادفی 2 گروه آزمایش و1 کنترل (هر کدام 15 نفر) گمارده شدند. ابزار اندازه‌گیری شامل پرسشنامه‌های (بوند همکاران، 2011) هیجانی(مارس، 1983) بو...

T cells of the immune system, upon maturation, differentiate into either Th1 or Th2 cells that have different functions. The decision to which cell type to differentiate depends on the concentrations of transcription factors T-bet (x1) and GATA-3 (x2). The population density of the T cells, φ(t, x1, x2), satisfies a conservation law ∂φ/∂t+(∂/∂x1)(f1φ)+ (∂/∂x2)(f2φ) = gφ where fi depends on (t, ...

A complex number is nothing more than a point in the xy–plane. The first component, x, of the complex number (x, y) is called its real part and the second component, y, is called its imaginary part, even though there is nothing imaginary about it. The sum and product of two complex numbers (x1, y1) and (x2, y2) is defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) (x1, y1) (x2, y2) = (x1x2 − y...