Abstract
We prove several results relating injective one-way functions, time-bounded conditional Kolmogorov complexity, and time-bounded conditional entropy. First we establish a connection between injective, strong and weak one-way functions and the expected value of the polynomial time-bounded Kolmogorov complexity, denoted here by E(K-t (x vertical bar f (x))). These results are in both directions. More precisely, conditions on E(K-t (x vertical bar f (x))) that imply that f is a weak one-way function, and properties of E(K-t (x vertical bar f (x))) that are implied by the fact that f is a strong one-way function. In particular, we prove a separation result: based on the concept of time-bounded Kolmogorov complexity, we find an interval in which every function f is a necessarily weak but not a strong one-way function. Then we propose an individual approach to injective one-way functions based on Kolmogorov complexity, defining Kolmogorov one-way functions and prove some relationships between the new proposal and the classical definition of one-way functions, showing that a Kolmogorov one-way function is also a deterministic one-way function. A relationship between Kolmogorov one-way functions and the conjecture of polynomial time symmetry of information is also proved. Finally, we relate E(K-t (x vertical bar f (x))) and two forms of time-bounded entropy, the unpredictable entropy H-unp, in which "one-wayness" of a function can be easily expressed, and the Yao(+) entropy, a measure based on compression/decompression schema in which only the decompressor is restricted to be time-bounded.

Abstract
Sophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string that is shortest within some precision; the second can be defined as the minimal computation time of a program that is shortest within some precision. We show that the Busy Beaver function of the sophistication of a string exceeds its logical depth with logarithmically bigger precision, and that logical depth exceeds the Busy Beaver function of sophistication with logarithmically bigger precision. We also show that sophistication is unstable in its precision: constant variations can change its value by a linear term in the length of the string.

Abstract
We introduced a new method for distinguishing two probability ensembles called one from each method, in which the distinguisher receives as input two samples, one from each ensemble. We compare this new method with multi-sample from the same method already exiting in the literature and prove that there are ensembles distinguishable by the new method, but indistinguishable by the multi-sample from the same method. To evaluate the power of the proposed method we also show that if non-uniform distinguishers (probabilistic circuits) are used, the one from each method is not more powerful than the classical one, in the sense that does not distinguish more probability ensembles. Moreover we obtain that there are classes of ensembles, such that any two members of the class are easily distinguishable (a definition introduced in this paper) using one sample from each ensemble; there are pairs of ensembles in the same class that are indistinguishable by multi-sample from the same method.

Abstract
Objectives To characterise the test ordering pattern in Northern Portugal and to investigate the influence of context-related factors, analysing the test ordered at the level of geographical groups of family physicians and at the level of different healthcare organisations. Design Cross-sectional study. Setting Northern Primary Health Care, Portugal. Participants Records about diagnostic and laboratory tests ordered from 2035 family physicians working at the Northern Regional Health Administration, who served approximately 3.5 million Portuguese patients, in 2014. Outcomes To determine the 20 most ordered diagnostic and laboratory tests in the Northern Regional Health Administration; to identify the presence and extent of variations in the 20 most ordered diagnostic and laboratory tests between the Groups of Primary Care Centres and between health units; and to study factors that may explain these variations. Results The 20 most ordered diagnostic and laboratory tests almost entirely comprise laboratory tests and account for 70.9% of the total tests requested. We can trace a major pattern of test ordering for haemogram, glucose, lipid profile, creatinine and urinalysis. There was a significant difference (P<0.001) in test orders for all tests between Groups of Primary Care Centres and for all tests, except glycated haemoglobin (P=0.06), between health units. Generally, the Personalised Healthcare Units ordered more than Family Health Units. Conclusions The results from this study show that the most commonly ordered tests in Portugal are laboratory tests, that there is a tendency for overtesting and that there is a large variability in diagnostic and laboratory test ordering in different geographical and organisational Portuguese primary care practices, suggesting that there may be considerable potential for the rationalisation of test ordering. The existence of Family Health Units seems to be a strong determinant in decreasing test ordering by Portuguese family physicians. Approaches to ensuring more rational testing are needed.

Abstract
In this study, fetal heart rate signal is used to exemplify the performance of compression and entropy based approaches in biometric identification. A total of 167 pairs of traces from real fetus are analyzed under the popular normalized compression distance, the recently proposed normalized relative compression measure and mutual information measure. The best performance was achieved with the normalized compression distance resulting in a misclassification rate of 12%. Fetal heart rate could be a relevant feature for biometric identification models, namely in multiple pregnancies. © 2018 IEEE.

Abstract
In a witness hiding protocol the prover tries to convince the verifier that he knows a witness to an instance of an NP problem without revealing the witness. We propose a new look at witness hiding based on the information conveyed in each particular instance of the protocol. We introduce the concept of individual witness hiding (IWH) and prove that zero-knowledge protocols for classical problems like HAM are not IWH. On the other hand, we show that all FewP problems have an IWH protocol. Finally, by introducing a Kolmogorov string commitment protocol we can show that all FewP problems have an IWH protocol that is zero-knowledge relative to an oracle.