The contribution of human capital to the performance of Knowledge-Intensive Business Services

Purpose: The purpose of this paper is to investigate the relation between human capital and the performance of the various types of knowledge-intensive business services (KIBS). Research Methodology: The analysis conducted on business services industry level took into account the role of education in knowledge transfer, a major factor enriching the KIBS industry. A conceptual framework based on cluster analysis (CA) and classification and regression trees (CART) was developed to analyse human capital, the main asset in the KIBS sector (according to the resource-based theory), and its relations with the performance of KIBS providers. Results: The results pointed to the significant differences between various types of knowledge-based services. Findings suggest that there could be applied additional approach to classifying the KIBS services into three clusters according to the business characteristics (including human capital). Our third cluster closely related to human capital (HC) and information and communication technologies (ICT) demonstrated the best business performance. The results confirmed that KIBS providers with high average remuneration and high wage growth dynamic noted over doubled performance indicator (measured as profit growth). In that group of KIBS providers were (a) Software and IT companies, (b) Temporary employment agency activities and (c) Other human resources provision. Limitations: Our analysis is based on statistical data gathered by a public entity covered 3125 firms aggregated into twenty service types, which limits the scope of the research questions. Contribution: This study contributes to the state of knowledge of the performance dynamics of the various business services. Keywords: Business Services (BS), Human Capital (HC), Performance, Knowledge, Educatio

A Rough Set-Based Model of HIV-1 Reverse Transcriptase Resistome

Reverse transcriptase (RT) is a viral enzyme crucial for HIV-1 replication. Currently, 12 drugs are targeted against the RT. The low fidelity of the RT-mediated transcription leads to the quick accumulation of drug-resistance mutations. The sequence-resistance relationship remains only partially understood. Using publicly available data collected from over 15 years of HIV proteome research, we have created a general and predictive rule-based model of HIV-1 resistance to eight RT inhibitors. Our rough set-based model considers changes in the physicochemical properties of a mutated sequence as compared to the wild-type strain. Thanks to the application of the Monte Carlo feature selection method, the model takes into account only the properties that significantly contribute to the resistance phenomenon. The obtained results show that drug-resistance is determined in more complex way than believed. We confirmed the importance of many resistance-associated sites, found some sites to be less relevant than formerly postulated and—more importantly—identified several previously neglected sites as potentially relevant. By mapping some of the newly discovered sites on the 3D structure of the RT, we were able to suggest possible molecular-mechanisms of drug-resistance. Importantly, our model has the ability to generalize predictions to the previously unseen cases. The study is an example of how computational biology methods can increase our understanding of the HIV-1 resistome

Molecular markers (c-erbB-2, p53) in breast cancer.

The aim of our study was to evaluate the correlation between clinical characteristics, histopatologic features and c-erbB-2 as well as p53 expression in cancer tissues. Breast cancer tissue was obtained from 184 female subjects with primary breast cancer. According to hormonal status patients were divided into two groups - 64 belonged to the premenopausal group and 120 to postmenopausal group. Each patient underwent mammectomy and axillary lymphadenectomy. c-erbB-2 protooncogene was detected in 54% cases, and was correlated with infiltrating type of cancer growth, as well as larger tumor size. The presence of p53 antioncogene was observed only in 33% of cases, mainly in infiltrating duct carcinomas. The incidence of c-erbB-2 and p53 positive cases was higher among subjects, whose ultrasound and mammography revealed malignancy. There was no correlation found between of c-erbB-2 expression and axillary lymph nodes involvement It seems probable, that c-erbB-2 and p53 status of cancer tissue may prove to be useful in assessment of the level of biological aggressiveness in breast carcinomas and hence can be used as a prognostic factor

Representation of the Fibonacci and Lucas Numbers in Terms of Floor and Ceiling

In the paper we show how to express the Fibonacci numbers and Lucas numbers using the floor and ceiling operations.Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, PolandGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Piotr Rudnicki. Two programs for SCM. Part I - preliminaries. Formalized Mathematics, 4(1):69-72, 1993.Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin's test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Robert M. Solovay. Fibonacci numbers. Formalized Mathematics, 10(2):81-83, 2002.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Piotr Wojtecki and Adam Grabowski. Lucas numbers and generalized Fibonacci numbers. Formalized Mathematics, 12(3):329-333, 2004

Counting Derangements, Non Bijective Functions and the Birthday Problem

The article provides counting derangements of finite sets and counting non bijective functions. We provide a recursive formula for the number of derangements of a finite set, together with an explicit formula involving the number e. We count the number of non-one-to-one functions between to finite sets and perform a computation to give explicitely a formalization of the birthday problem. The article is an extension of [10].Institut für Informatik I4, Technische Universität München, Boltzmannstraße 3 85748 Garching, GermanyGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Yatsuka Nakamura and Hisashi Ito. Basic properties and concept of selected subsequence of zero based finite sequences. Formalized Mathematics, 16(3):283-288, 2008, doi:10.2478/v10037-008-0034-y.Karol Pąk. Cardinal numbers and finite sets. Formalized Mathematics, 13(3):399-406, 2005.Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998

The Perfect Number Theorem and Wilson's Theorem

This article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson's theorem (that n is prime iff n > 1 and (n - 1)! ≅ -1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler's sum of divisors function Φ, proves that Φ is multiplicative and that Σ k|n Φ(k) = n.Casella Postale 49, 54038 Montignoso, ItalyM. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004.Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Yoshinori Fujisawa and Yasushi Fuwa. The Euler's function. Formalized Mathematics, 6(4):549-551, 1997.Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin's test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Krzysztof Hryniewiecki. Recursive definitions. Formalized Mathematics, 1(2):321-328, 1990.Magdalena Jastrzebska and Adam Grabowski. On the properties of the Möbius function. Formalized Mathematics, 14(1):29-36, 2006, doi:10.2478/v10037-006-0005-0.Artur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179-186, 2004.Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.W. J. LeVeque. Fundamentals of Number Theory. Dover Publication, New York, 1996.Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Piotr Rudnicki. Little Bezout theorem (factor theorem). Formalized Mathematics, 12(1):49-58, 2004.Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Hiroshi Yamazaki, Yasunari Shidama, and Yatsuka Nakamura. Bessel's inequality. Formalized Mathematics, 11(2):169-173, 2003

Basel Problem – Preliminaries

SummaryIn the article we formalize in the Mizar system [4] preliminary facts needed to prove the Basel problem [7, 1]. Facts that are independent from the notion of structure are included here.Korniłowicz Artur - Institute of Informatics, University of Białystok, PolandPąk Karol - Institute of Informatics, University of Białystok, PolandM. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-817.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.Augustin Louis Cauchy. Cours d’analyse de l’Ecole royale polytechnique. de l’Imprimerie royale, 1821.Wenpai Chang, Yatsuka Nakamura, and Piotr Rudnicki. Inner products and angles of complex numbers. Formalized Mathematics, 11(3):275–280, 2003.Wenpai Chang, Hiroshi Yamazaki, and Yatsuka Nakamura. The inner product and conjugate of finite sequences of complex numbers. Formalized Mathematics, 13(3):367–373, 2005.Noboru Endou. Double series and sums. Formalized Mathematics, 22(1):57–68, 2014. doi: 10.2478/forma-2014-0006.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from ℝ to ℝ and integrability for continuous functions. Formalized Mathematics, 9(2):281–284, 2001.Adam Grabowski and Yatsuka Nakamura. Some properties of real maps. Formalized Mathematics, 6(4):455–459, 1997.Artur Korniłowicz and Yasunari Shidama. Inverse trigonometric functions arcsin and arccos. Formalized Mathematics, 13(1):73–79, 2005.Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703–709, 1990.Xiquan Liang and Bing Xie. Inverse trigonometric functions arctan and arccot. Formalized Mathematics, 16(2):147–158, 2008. doi: 10.2478/v10037-008-0021-3.Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455–460, 2001.Keiichi Miyajima and Takahiro Kato. The sum and product of finite sequences of complex numbers. Formalized Mathematics, 18(2):107–111, 2010. doi: 10.2478/v10037-010-0014-x.Cuiying Peng, Fuguo Ge, and Xiquan Liang. Several integrability formulas of special functions. Formalized Mathematics, 15(4):189–198, 2007. doi: 10.2478/v10037-007-0023-6.Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125–130, 1991.Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787–791, 1990.Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335–338, 1997.Yasunari Shidama, Noboru Endou, and Katsumi Wasaki. Riemann indefinite integral of functions of real variable. Formalized Mathematics, 15(2):59–63, 2007. doi: 10.2478/v10037-007-0007-6.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445–449, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255–263, 1998.25214114