Một số cải tiến cho các kiểm tra thống kê tính ngẫu nhiên sử dụng so khớp mẫu

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Mối liên hệ giữa tính nhận biết tiền ảnh và một số tính chất mật mã khác của hàm băm

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Preliminary evidence for the Matrix Matching Test as a valid and reliable measure of general cognitive ability in adolescents

Introduction: In research, a simple measure of general cognitive ability is often required. One method is the Matrix Matching Test, a brief, free-to-use, language-free assessment of general cognitive ability or intelligence in adults, which taps both fluid and crystalized processes. We investigated its reliability and validity with adolescent participants. Method:The Matrix Matching Test was administered to 111 participants, aged 12 to 17 (46% female).Subsamples also completed two standard measures of cognitive ability: Vocabulary (crystalized) and Matrix Reasoning (fluid) tests from the Wechsler Intelligence Scale for Children IV (WISC-IV). Results: The Matrix Matching Test was found to have acceptable internal consistency and good retest reliability. Criterion validity was indicated by its ability to distinguish between psychosocially deprived participants living in foster care (n = 40) and controls, and by its positive correlation with grade point average. There were large positive correlations between the Matrix Matching Test and the standard measures of Vocabulary, and Matrix Reasoning, suggesting convergent validity. Conclusions: Our preliminary evidence suggests that The Matrix Matching Test is a reliable and valid measure of general cognitive ability for ages 12 to 17.

Randomness of Möbius coefficients and Brownian motion: growth of the Mertens function and the Riemann hypothesis

The validity of the Riemann hypothesis (RH) on the location of the non-trivial zeros of the Riemann ζ-function is directly related to the growth of the Mertens function M ( x ) = ∑ k = 1 x μ ( k ) , where μ(k) is the Möbius coefficient of the integer k; the RH is indeed true if the Mertens function goes asymptotically as M(x) ∼ x 1/2+ϵ , where ϵ is an arbitrary strictly positive quantity. We argue that this behavior can be established on the basis of a new probabilistic approach based on the global properties of the Mertens function, namely, based on reorganizing globally in distinct blocks the terms of its series. With this aim, we focus attention on the square-free numbers and we derive a series of probabilistic results concerning the prime number distribution along the series of square-free numbers, the average number of prime divisors, the Erdős–Kac theorem for square-free numbers, etc. These results point to the conclusion that the Mertens function is subject to a normal distribution as much as any other random walk. We also present an argument in favor of the thesis that the validity of the RH also implies the validity of the generalized RH for the Dirichlet L-functions. Next we study the local properties of the Mertens function, i.e. its variation induced by each Möbius coefficient restricted to the square-free numbers. Motivated by the natural curiosity to see how closely to a purely random walk any sub-sequence is extracted by the sequence of the Möbius coefficients for the square-free numbers, we perform a massive statistical analysis on these coefficients, applying to them a series of randomness tests of increasing precision and complexity; together with several frequency tests within a block, the list of our tests includes those for the longest run of ones in a block, the binary matrix rank test, the discrete Fourier transform test, the non-overlapping template matching test, the entropy test, the cumulative sum test, the random excursion tests, etc, for a total of 18 different tests. The successful outputs of all these tests (each of them with a level of confidence of 99% that all the sub-sequences analyzed are indeed random) can be seen as impressive ‘experimental’ confirmations of the Brownian nature of the restricted Möbius coefficients and the probabilistic normal law distribution of the Mertens function analytically established earlier. In view of the theoretical probabilistic argument and the large battery of statistical tests, we can conclude that while a violation of the RH is strictly speaking not impossible, it is however extremely improbable.

Use of the Oxford Face Matching Test Reveals an Effect of Ageing on Face Perception but Not Face Memory.

Effects of ageing on both face perception and face memory have previously been reported. Previous studies, however, have not controlled for the effects of face perception when assessing face memory, meaning that apparent effects of ageing on face memory may actually be due to effects of ageing on face perception. Here, both face perception and face memory were assessed in a sample of adults ranging in age from 18 to 93, and the effect of age on face memory was assessed after controlling for face perception. Face perception was assessed using both a standard test and the Oxford Face Matching Test (OFMT), deliberately designed to avoid the bias towards younger, neurotypical samples that may be present in other tests. An effect of ageing on face perception was found using both tests, with the unbiased OFMT being more sensitive to the effect of age. Importantly, when controlling for face perception using the OFMT, no effect of age on face memory was found. Indicative scores on the OFMT from a sample of 989 participants are provided, broken down by age and gender.

The Oxford Face Matching Test: A non-biased test of the full range of individual differences in face perception

Tests of face processing are typically designed to identify individuals performing outside of the typical range; either prosopagnosic individuals who exhibit poor face processing ability, or super recognisers, who have superior face processing abilities. Here we describe the development of the Oxford Face Matching Test (OFMT), designed to identify individual differences in face processing across the full range of performance, from prosopagnosia, through the range of typical performance, to super recognisers. Such a test requires items of varying difficulty, but establishing difficulty is problematic when particular populations (e.g., prosopagnosics, individuals with autism spectrum disorder) may use atypical strategies to process faces. If item difficulty is calibrated on neurotypical individuals, then the test may be poorly calibrated for atypical groups, and vice versa. To obtain items of varying difficulty, we used facial recognition algorithms to obtain face pair similarity ratings that are not biased towards specific populations. These face pairs were used as stimuli in the OFMT, and participants were required to judge whether the face images depicted the same individual or different individuals. Across five studies the OFMT was shown to be sensitive to individual differences in the typical population, and in groups of both prosopagnosic individuals and super recognisers. The test-retest reliability of the task was at least equivalent to the Cambridge Face Memory Test and the Glasgow Face Matching Test. Furthermore, results reveal, at least at the group level, that both face perception and face memory are poor in those with prosopagnosia, and are good in super recognisers.

It Works Without Words

Emotion recognition ability of emotions expressed by other people (ERA-O) can be important for job performance, leadership, bargaining, and career success. Traditional personnel assessment tools of this ability, however, are contaminated by linguistic skills. In a time of global work migration, more and more people speak a language at work that is not their mother tongue. Consequently, we developed and validated the Face-Based Emotion Matching Test (FEMT), a nonlinguistic objective test of ERA-O in gainfully employed adults. We demonstrate the FEMT’s validity with psychological constructs (cognitive and emotional intelligence, Big Five personality traits) and its criterion validity and interethnic fit.

The Jena Voice Learning and Memory Test (JVLMT): A standardized tool for assessing the ability to learn and recognize voices

The ability to recognize someone’s voice exists on a broad spectrum with phonagnosia on the low end and super recognition at the high end. Yet there is no standardized test to measure an individual’s ability of learning and recognizing newly-learnt voices with samples of speech-like phonetic variability. We have developed the Jena Voice Learning and Memory Test (JVLMT), a 22min-test based on item response theory and applicable across languages. The JVLMT consists of three phases in which participants first become familiarized with eight speakers and then perform a three-alternative forced choice recognition task, using pseudo sentences devoid of semantics. Acoustic (dis)similarity analyses were used to create items with different levels of difficulty. Test scores are based on 22 Rasch-conform items. Items were selected based on 232 and validated based on 454 participants in an online study. Mean accuracy is 0.51 with an SD of .18. The JVLMT showed high and moderate correlations with the convergent validation tests (Bangor Voice Matching Test; Glasgow Voice Memory Test, respectively) and a weak correlation with the discriminant validation test (Digit Span). Empirical (marginal) reliability is 0.66. Four participants with super recognition abilities and 7 participants with phonagnosia were identified (at least 2 SDs above or below the mean, respectively).The JVLMT is a promising diagnostic tool to screen for voice recognition abilities in a scientific and neuropsychological context.