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1
Liu, Wen Feng, Xing Pan Fu, and Jie Ying Sui. "Probability Analyses of Response Spectra on Soft Soil Site." Advanced Materials Research 261-263 (May 2011): 1058–63. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.1058.
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The analyses on the statistical probability of the response spectra have an important role in determining the earthquake demand. Elastic and inelastic spectra on acceleration of the 369 records with a long characteristic period for SDOF systems were presented in statistical analyses. The empirical probability distributions of the spectral values were derived according to the Kolmogorov-Smirnov (KS) goodness-of-fit test. And the spectra considering the probability guaranty were developed to investigate the characteristic of the response spectra. The formula for statistical average spectra of the ground motion ensemble were recommended, which were valuable for current research and code revisal. The results show:(1)the inelastic responses decrease with the increase of ductility demand μ when μ<4, and they decrease unclearly when μ≥4;(2) the inelastic spectra has a large value of Cov (coefficient of variance),the Cov range from 0.2 to 0.3 when T<1s,and it increases linearly when T≥1s;(3)the probabilistic distribution of the spectra value on acceleration is validated as the lognormal or the Gumbel type I distributions;(4) the probabilistic spectra may be a feasible way to determine earthquake load in the future.
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Aldous, David. "Hashing with Linear Probing under Nonuniform Probabilities." Probability in the Engineering and Informational Sciences 2, no. 1 (January 1988): 1–14. http://dx.doi.org/10.1017/s0269964800000577.
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Probabilistic analyses of hashing algorithms usually assume that hash values are uniformly distributed over addresses. We study how one of the simplest schemes, hashing with linear probing, behaves in the nonuniform case. A simple measure μ of nonuniformity is the probability two keys hash to the same address, divided by this probability in the uniform case. It turns out that the effect of nonuniformity is to multiply mean search lengths by μ. For high loads, the longest search is multiplied by approximately μ also. Our theoretical results are asymptotics: simulations show good fits with predictions for mean search lengths, but bad fits for longest search lengths.
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Field, R. V., P. G. Voulgaris, and L. A. Bergman. "Methods to Compute Probabilistic Measures of Robustness for Structural Systems." Journal of Vibration and Control 2, no. 4 (October 1996): 447–63. http://dx.doi.org/10.1177/107754639600200405.
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Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst- case analyses. These traditional methods include the use of the structured singular value (μ-analysis), as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. Because of this, an attempt to view controller robustness as a probability measure is presented. As a result, a much more intuitive insight into controller robustness can be obtained. In this context, the joint probability distribution is of dimension equal to the number of uncertain parameters, and the failure hypersurface is defined by the onset of instability of the closed-loop system in the eigenspace. A first-order reliability measure (FORM) of the system is computed and used to estimate controller robustness. It is demonstrated via an example that this FORM method can provide accurate results on the probability of failure despite the potential complexity of the closed-loop. In addition to the FORM method, a probabilistic measure of robustness is developed based on the fundamentals of μ-analysis. It is shown that the μ-analysis based method is inferior to the FORM method and can only have qualitative value when assessing control system robustness in a probabilistic framework.
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Liu, Wen Feng, Xue Zhong Chen, and Jie Ying Sui. "Statistical Analyses of Response Spectra on Medium-Stiff Soil Site." Applied Mechanics and Materials 90-93 (September 2011): 1549–54. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.1549.
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The analyses on the statistical response spectra have an important role in determining the earthquake demand. Elastic and inelastic spectra on acceleration of the 205 records on medium-stiff soil site for SDOF systems are presented in statistical analyses. The empirical probability distributions of the spectral values are derived according to the Kolmogorov-Smirnov (KS) goodness-of-fit test. The formula for statistical average spectra of the ground motion ensemble are recommended, which are valuable for current research and code revisal. The results show that the statistical averaged elastic α spectra fits well to the design spectra prescribed in Chinese code when the period is smaller than 2s. The inelastic responses decrease with the increase of ductility demand μ when μ<4. The coefficients of variance of the elastic and inelastic spectra are still large and the dispersion cannot be ignored. The probabilistic distribution of the spectra value on acceleration is validated as the lognormal distributions. The proposed formulas give a good fit to the statistical average values.
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Brango, Hugo, Angie Guerrero, and Humberto Llinás. "Marshall–Olkin Bivariate Weibull Model with Modified Singularity (MOBW-μ): A Study of Its Properties and Correlation Structure." Mathematics 12, no. 14 (July 11, 2024): 2183. http://dx.doi.org/10.3390/math12142183.
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We propose the “Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW-μ”, which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW-μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW-μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW-μ does not have the Lancaster’s phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines.
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AUSTIN, TIM. "On the norm convergence of non-conventional ergodic averages." Ergodic Theory and Dynamical Systems 30, no. 2 (June 23, 2009): 321–38. http://dx.doi.org/10.1017/s014338570900011x.
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AbstractWe offer a proof of the following non-conventional ergodic theorem: If Ti:ℤr↷(X,Σ,μ) for i=1,2,…,d are commuting probability-preserving ℤr-actions, (IN)N≥1 is a Følner sequence of subsets of ℤr, (aN)N≥1 is a base-point sequence in ℤr and f1,f2,…,fd∈L∞(μ) then the non-conventional ergodic averages converge to some limit in L2(μ) that does not depend on the choice of (aN)N≥1 or (IN)N≥1. The leading case of this result, with r=1 and the standard sequence of averaging sets, was first proved by Tao, following earlier analyses of various more special cases and related results by Conze and Lesigne, Furstenberg and Weiss, Zhang, Host and Kra, Frantzikinakis and Kra and Ziegler. While Tao’s proof rests on a conversion to a finitary problem, we invoke only techniques from classical ergodic theory, so giving a new proof of his result.
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DIETZFELBINGER, MARTIN, JONATHAN E. ROWE, INGO WEGENER, and PHILIPP WOELFEL. "Tight Bounds for Blind Search on the Integers and the Reals." Combinatorics, Probability and Computing 19, no. 5-6 (December 18, 2009): 711–28. http://dx.doi.org/10.1017/s0963548309990599.
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We analyse a simple random process in which a token is moved in the interval A = {0, . . ., n}. Fix a probability distribution μ over D = {1, . . ., n}. Initially, the token is placed in a random position in A. In round t, a random step sized is chosen according to μ. If the token is in position x ≥ d, then it is moved to position x − d. Otherwise it stays put. Let TX be the number of rounds until the token reaches position 0. We show tight bounds for the expectation Eμ(TX) of TX for varying distributions μ. More precisely, we show that $\min_\mu\{\E_\mu(T_X)\}=\Theta\bigl((\log n)^2\bigr)$. The same bounds are proved for the analogous continuous process, where step sizes and token positions are real values in [0, n + 1), and one measures the time until the token has reached a point in [0, 1). For the proofs, a novel potential function argument is introduced. The research is motivated by the problem of approximating the minimum of a continuous function over [0, 1] with a ‘blind’ optimization strategy.
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Hao, Yiqing, Hao Lu, Yehui Shi, Hao Geng, Xi J, and Shufang Feng. "Uncertainty Evaluation of Water Inrush in Karst Tunnels Based on Epistemic Uncertainty with Possibility Theory." Mathematical Problems in Engineering 2020 (August 6, 2020): 1–12. http://dx.doi.org/10.1155/2020/2819797.
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In the risk assessment of water inrush in karst tunnel, it is most important to provide an available theoretical model for qualifying the epistemic uncertainties due to a lack of knowledge and information. Firstly, a mechanical model dependent on geology is introduced associating with four parameters, i.e., the elastic modulus E, the Poisson ratio μ, the water differential pressure q, and the tunnel radius a. Then, a mathematical model representing epistemic uncertainty is represented with probability theory and possibility theory. The methodology was computerized to calculate the distribution of the margin and uncertainty and then to determine the ratio of “margin/uncertainty.” Analyses involving possibility theory and possibility theory are illustrated with the same engineering example used in the presentation indicated above to illustrate the use of probability to represent aleatory and epistemic uncertainty in QMU analyses. The comparison between the uses of possibility theory and probability theory for the representation of aleatory and epistemic uncertainty indicates that the possibility is not only has a better mathematical structure than probability theory but also has some challenges.
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Pinus, B. I., I. G. Korneeva, and V. D. Balheeva. "Fatigue life of bending reinforced concrete elements with fibre-reinforced matrices." Journal «Izvestiya vuzov. Investitsiyi. Stroyitelstvo. Nedvizhimost» 12, no. 3 (2022): 362–67. http://dx.doi.org/10.21285/2227-2917-2022-3-362-367.
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An experimental-probabilistic analysis of variations in the load-bearing capacity of bending reinforced concrete elements with matrices reinforced by polypropylene fibres was carried out. A numerical ex-periment was conducted using the normative methodology of multi-link and layerwise modelling of el-ement cross-sections and experimental "σ-ε" diagrams of fibrocomposites in initial and post-cyclic (50 cycles with η = 0.8 amplitude and zero asymmetry) states. Probabilistic changes in the load-bearing capacity of bending elements subjected to cyclic loads were estimated by the numerical strength modelling of rectangular beams (b × h = 100 × 200 mm) with the one-sided reinforcement (A400 class) of varying intensity. The observed high value of fatigue life of reinforced concrete ele-ments with fibre-reinforced matrices was found to be associated with the presence of mechanisms compensatory for structural changes, i.e., a decrease in the strength is accompanied by an increase in the ability to redistribute internal forces. A post-cyclic reduction in the strength of concrete causes practically no effect on the load-bearing capacity of bending elements with a large and economically preferable range of their structural reinforcement. The reliability kinetics of elements, estimated by the level of the realised concrete strength potential, was analysed. Moderate (μ ≤ μR) reinforcement was found to result in objective conditions for increasing the completeness of the stress diagram in the compressed cross-sectional part due to the redistribution of forces along the height. In this case, de-spite a significant decrease in the strength of concrete, the load-bearing capacity of elements at μ ≤ 2.5% reinforcement remains practically the same after cyclic effects.
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Lou, Yi, Ruofan Sun, Julian Cheng, Gang Qiao, and Jinlong Wang. "Physical-Layer Security for UAV-Assisted Air-to-Underwater Communication Systems with Fixed-Gain Amplify-and-Forward Relaying." Drones 6, no. 11 (November 3, 2022): 341. http://dx.doi.org/10.3390/drones6110341.
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We analyze a secure unmanned aerial vehicle-assisted two-hop mixed radio frequency (RF) and underwater wireless optical communication (UWOC) system using a fixed-gain amplify-and-forward (AF) relay. The UWOC channel was modeled using a mixture exponential-generalized Gamma distribution to consider the combined effects of air bubbles and temperature gradients on transmission characteristics. Both legitimate and eavesdropping RF channels were modeled using flexible α-μ distributions. Specifically, we first derived both the probability density function (PDF) and cumulative distribution function (CDF) of the received signal-to-noise ratio of the system. Based on the PDF and CDF expressions, we derived the closed-form expressions for the tight lower bound of the secrecy outage probability (SOP) and the probability of non-zero secrecy capacity (PNZ), which are both expressed in terms bivariate Fox’s H-function. To utilize these analytical expressions, we derived asymptotic expressions of SOP and PNZ using only well-known functions. We also used asymptotic expressions to determine the suboptimal transmitting power to maximize energy efficiency. Furthermore, we investigated the effect of levels of air bubbles and temperature gradients in the UWOC channel, and studied the nonlinear characteristics of the transmission medium and the number of multipath clusters of the RF channel on the secrecy performance. Finally, all analyses were validated using a simulation.
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Schreiber, Tomasz. "Asymptotic geometry of high-density smooth-grained Boolean models in bounded domains." Advances in Applied Probability 35, no. 4 (December 2003): 913–36. http://dx.doi.org/10.1239/aap/1067436327.
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The purpose of the paper is to study the asymptotic geometry of a smooth-grained Boolean model (X[t])t≥0 restricted to a bounded domain as the intensity parameter t goes to ∞. Our approach is based on investigating the asymptotic properties as t → ∞ of the random sets X[t;β], β≥0, defined as the Gibbsian modifications of X[t] with the Hamiltonian given by βtμ(·), where μ is a certain normalized measure on the setting space. We show that our model exhibits a phase transition at a certain critical value of the inverse temperature β and we prove that at higher temperatures the behaviour of X[t;β] is qualitatively very similar to that of X[t] but it becomes essentially different in the low-temperature region. From these facts we derive information about the asymptotic properties of the original process X[t]. The results obtained include large- and moderate-deviation principles. We conclude the paper with an example application of our methods to analyse the asymptotic moderate-deviation properties of convex hulls of large uniform samples on a multidimensional ball. To translate the above problem to the Boolean model setting considered we use an appropriate representation of convex sets in terms of their support functions.
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Nithya, M., Gyanendra Prasad Joshi, C. Sugapriya, S. Selvakumar, N. Anbazhagan, Eunmok Yang, and Ill Chul Doo. "Analysis of Stochastic State-Dependent Arrivals in a Queueing-Inventory System with Multiple Server Vacation and Retrial Facility." Mathematics 10, no. 17 (August 23, 2022): 3041. http://dx.doi.org/10.3390/math10173041.
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This article analyses a four-dimensional stochastic queueing-inventory system with multiple server vacations and a state-dependent arrival process. The server can start multiple vacations at a random time only when there is no customer in the waiting hall and the inventory level is zero. The arrival flow of customers in the system is state-dependent. Whenever the arriving customer finds that the waiting hall is full, they enter into the infinite orbit and they retry to enter the waiting hall. If there is at least one space in the waiting hall, the orbital customer enters the waiting hall. When the server is on vacation, the primary (retrial) customer enters the system with a rate of λ1(θ1). If the server is not on vacation, the primary (retrial) arrival occurs with a rate of λ2(θ2). Each arrival rate follows an independent Poisson distribution. The service is provided to customers one by one in a positive time with the rate of μ, which follows exponential distribution. When the inventory level drops to a fixed s, reorder of Q items is triggered immediately under (s,Q) ordering policy. The stability of the system has been analysed, and using the Neuts matrix geometric approach, the stationary probability vectors have been obtained. Moreover, various system performance measures are derived. The expected total cost analysis explores and verifies the characteristics of the assumed parameters of this model. The average waiting time of a customer in the waiting hall and orbit are investigated using all the parameters. The monotonicity of the parameters is verified with its characteristics by the numerical simulation. The discussion about the fraction time server being on vacation suggests that as the server’s vacation duration reduces, its fraction time also reduces. The mean number of customers in the waiting hall and orbit is reduced whenever the average service time per customer and average replenishment time are reduced.
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Prinz, Aloys, and David J. Richter. "Feinstaubbelastung und Lebenserwartung in Deutschland." AStA Wirtschafts- und Sozialstatistisches Archiv 15, no. 3-4 (November 19, 2021): 237–72. http://dx.doi.org/10.1007/s11943-021-00292-1.
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ZusammenfassungDie Feinstaubbelastung steht immer wieder im Mittelpunkt umwelt- und gesundheitspolitischer Diskussionen. Empirische Analysen, auch solche in diesem Bereich, die nicht auf individuellen Experimentaldaten beruhen, können als ökologische „real life“-Studien kleine Bausteine zum Verständnis der Zusammenhänge von Feinstaubbelastung und deren Gesundheitsfolgen zur Verfügung stellen. In diesem Beitrag wird deskriptiv untersucht, ob in Deutschland eine Korrelation von Feinstaubbelastung und Lebenserwartung zu finden ist. Dazu werden auf Kreisebene nach den Messbereichen Hintergrund und Verkehr differenzierte Daten von Feinstaubmessstationen der Jahre 2002 bis 2016 verwendet. Als weitere Kovariate der Lebenserwartung werden auf Kreisebene das verfügbare Einkommen pro Kopf und die Abiturientenquote berücksichtigt. Darüber hinaus werden Siedlungseigenschaften (städtische bzw. ländliche Gebiete) sowie ein nichtlinearer Zeittrend in die Untersuchung einbezogen. Die Niveauschätzungen ergeben einen negativen Zusammenhang für die Feinstaubbelastung im westdeutschen Hintergrundbereich. Darüber hinaus zeigt sich ein negativer Zusammenhang zwischen der Veränderung von Feinstaubbelastung und der Veränderung der Lebenserwartung für den westdeutschen Verkehrsbereich, der jedoch aufgrund der Datenlage als unsicherer anzusehen ist. Letzteres ist aufgrund der Besonderheiten dieses Bereichs (tages- und jahreszeitlich bedingte Variationen des Verkehrsflusses; Änderung der Feinstaub-Exposition der Bevölkerung innerhalb kurzer Entfernungen u. v. m.) nicht überraschend. Für Ostdeutschland konnten keine statistisch signifikanten Zusammenhänge gefunden werden. Die für Gesamtdeutschland gefundene Korrelation zwischen Feinstaubbelastung im Hintergrundbereich und durchschnittliche Lebenserwartung liegt bei 0,037 Jahre pro 1 $$\upmu$$ μ g/m$${}^{3}$$ 3 PM$${}_{10}$$ 10 .
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Mohan, Manu, Sambandam Sathyakumar, and Ramesh Krishnamurthy. "Predator in proximity: how does a large carnivore respond to anthropogenic pressures at fine-scales? Implications for interface area management." PeerJ 12 (July 10, 2024): e17693. http://dx.doi.org/10.7717/peerj.17693.
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Background Driven by habitat loss and fragmentation, large carnivores are increasingly navigating human-dominated landscapes, where their activity is restricted and their behaviour altered. This movement, however, raises significant concerns and costs for people living nearby. While intricately linked, studies often isolate human and carnivore impacts, hindering effective management efforts. Hence, in this study, we brought these two into a common framework, focusing on an interface area between the critical tiger habitat and the human-dominated multiple-use buffer area of a central Indian protected area. Methods We employed a fine-scale camera trap survey complemented by GPS-collar movement data to understand spatio-temporal activity patterns and adjustments of tigers in response to anthropogenic pressures. We used an occupancy framework to evaluate space use, Bayesian circular GLMs to model temporal activity, and home range and step length analyses to assess the movement patterns of tigers. Further, we used predation-risk models to understand conflict patterns as a function of tiger presence and other habitat variables. Results Despite disturbance, a high proportion of the sampled area was occupied by 17 unique tigers (ψ = 0.76; CI [0.73–0.92]). The distance to villages (β ± SE = 0.63 ± 0.21) and the relative abundance of large-bodied wild prey (β ± SE = 0.72 ± 0.37) emerged as key predictors of tiger space use probability, indicating a preference for wild prey by tigers, while human influences constrained their habitat utilisation. Distance to villages was also identified as the most significant predictor of the tigers’ temporal activity (μ ± σ = 3.03 ± 0.06 rad) that exhibited higher nocturnality near villages. A total of 11% of tiger home ranges were within village boundaries, accompanied by faster movement in these areas (displacement 40–82% higher). Livestock depredation probability by tigers increased with proximity to villages (P = 0.002) and highway (P = 0.003). Although tiger space use probability (P = 0.056) and wild prey abundance (P = 0.134) were non-significant at the 0.05 threshold, their presence in the best-fit predation-risk model suggests their contextual relevance for understanding conflict risk. The results highlight the importance of appropriately managing livestock near human infrastructures to effectively mitigate conflict. Conclusions Shared space of carnivores and humans requires dynamic site-specific actions grounded in evidence-based decision-making. This study emphasises the importance of concurrently addressing the intricate interactions between humans and large carnivores, particularly the latter’s behavioural adaptations and role in conflict dynamics. Such an integrated approach is essential to unravel cause-effect relationships and promote effective interface management in human-dominated landscapes.
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Bialek, J., M. Dall Osto, P. Vaattovaara, S. Decesari, J. Ovadnevaite, A. Laaksonen, and C. O'Dowd. "Hygroscopic and chemical characterisation of Po Valley aerosol." Atmospheric Chemistry and Physics 14, no. 3 (February 12, 2014): 1557–70. http://dx.doi.org/10.5194/acp-14-1557-2014.
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Abstract. Continental summer-time aerosol in the Italian Po Valley was characterised in terms of hygroscopic properties and the influence of chemical composition therein. Additionally, the ethanol affinity of particles was analysed. The campaign-average minima in hygroscopic growth factors (HGFs, at 90% relative humidity) occurred just before and during sunrise from 03:00 to 06:00 LT (all data are reported in the local time), but, more generally, the hygroscopicity during the whole night is very low, particularly in the smaller particle sizes. The average HGFs recorded during the low HGF period were in a range from 1.18 (for the smallest, 35nm particles) to 1.38 (for the largest, 165 nm particles). During the day, the HGF gradually increased to achieve maximum values in the early afternoon hours 12:00–15:00, reaching 1.32 for 35 nm particles and 1.46 for 165 nm particles. Two contrasting case scenarios were encountered during the measurement period: Case 1 was associated with westerly air flow moving at a moderate pace and Case 2 was associated with more stagnant, slower moving air from the north-easterly sector. Case 1 exhibited weak diurnal temporal patterns, with no distinct maximum or minimum in HGF or chemical composition, and was associated with moderate non-refractory aerosol mass concentrations (for 50% size cut at 1 μ) of the order of 4.5 μg m−3. For Case 1, organics contributed typically 50% of the mass. Case 2 was characterised by >9.5 μg m−3 total non-refractory mass (<1 μ) in the early morning hours (04:00), decreasing to ~3 μg m−3 by late morning (10:00) and exhibited strong diurnal changes in chemical composition, particularly in nitrate mass but also in total organic mass concentrations. Specifically, the concentrations of nitrate peaked at night-time, along with the concentrations of hydrocarbon-like organic aerosol (HOA) and of semi-volatile oxygenated organic aerosol (SV-OOA). In general, organic growth factors (OGFs) followed a trend which was opposed to HGF and also to the total organic mass as measured by the aerosol mass spectrometer. The analysis of the HGF probability distribution function (PDF) reveals an existence of a predominant "more hygroscopic" (MH) mode with HGF of 1.5 around noon, and two additional modes: one with a "less hygroscopic" (LH) HGF of 1.26, and another with a "barely hygroscopic" (BH) mode of 1.05. Particles sized 165 nm exhibited moderate diurnal variability in HGF, ranging from 80% at night to 95% of "more hygroscopic" growth factors (i.e. HGFs 1.35–1.9) around noon. The diurnal changes in HGF progressively became enhanced with decreasing particle size, decreasing from 95% "more hygroscopic" growth factor fraction at noon to 10% fraction at midnight, while the "less hygroscopic" growth factor fraction (1.13–1.34) increased from 5% at noon to > 60% and the "barely hygroscopic" growth factor fraction (1.1–1.2) increased from less than 2% at noon to 30% at midnight. Surprisingly, the lowest HGFs occurred for the period when nitrate mass reached peak concentrations (Case 2). We hypothesised that the low HGFs of nitrate-containing particles can be explained by a) an organic coating suppressing the water-uptake, and/or by b) the existence of nitrates in a less hygroscopic state, e.g. as organic nitrates. The latter hypothesis allows us to explain also the reduced OGFs observed during the early morning hours (before dawn) when nitrate concentrations peaked, based on the evidence that organic nitrates have significant lower ethanol affinity than other SV-OOA compounds.
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Choe, Yong, Geraldine Baggs, Genevieve D'Annunzio, Alexandra Laliberte, and Kajzer Janice. "Projecting Infant Weight Gain per Day to 112 Days from First 35 Days of Life." Current Developments in Nutrition 4, Supplement_2 (May 29, 2020): 1163. http://dx.doi.org/10.1093/cdn/nzaa056_010.
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Abstract Objectives The American Academy of Pediatrics Task Force on Clinical Testing of Infant Formulas [1] stated, “Determination of rate of gain in weight is the single most valuable component of the clinical evaluation of an infant formula” and “recommends, that weight gain be determined over an interval of 3 to 4 months.” A gastrointestinal tolerance study (denoted ST) measured infants' weight gain per day from 14 to 35 days of age (CW2). The objectives of this project were 1) to estimate weight gain per day from 14 to 112 days of age (CW5) using the CW2 in ST and historical data from seven 4-months growth and tolerance studies by simulation and bootstrap, and 2) to determine if ST would have supported normal physical growth in infants had the study been continued to 112 days of age by showing that the experimental formula is non-inferior to the control formula using weight gain accretion of 3 g/day as the non-inferiority margin. 1. American Academy of Pediatrics, Committee on Nutrition, (CON-AAP). “Clinical Testing of Infant Formulas With Respect to Nutritional Suitability for Term Infants.” June 1988 (Report prepared under FDA contract 223-86-2117) (available at https://wayback.archive-it.org/7993/20170722090324/https://www.fda.gov/Food/GuidanceRegulation/GuidanceDocumentsRegulatoryInformation/InfantFormula/ucm170649.htm) (accessed May 23, 2019). Methods The simulation made use of the observed linear relationship between CW2 and CW5 from growth data in the historical studies, which included 16 formula groups. The simulated data for CW2 and CW5 were generated using multivariate normal distribution with mean vector μ and covariance matrix ∑, estimated from ST and the historical studies. In addition, the bootstrapped distribution of the difference in mean CW5 between the experimental and control groups in ST was derived using the historical studies. Software SAS® 9.4 and SAS® Enterprise Guide 7.1 (SAS Institute Inc, Cary, NC) were used for this report. Results Based on the analyses, we conclude that growth observed from 14 to 35 days of age in ST when extended to 112 days of age will demonstrate normal physical growth with high probability (> 98%). Conclusions Using such a predictive model may be a complementary solution for bridging growth and tolerance studies of shorter duration to 4 months for minor changes to infant formulas. Funding Sources Abbott Laboratories.
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Hayakawa, Satoshi, Harald Oberhauser, and Terry Lyons. "Hypercontractivity meets random convex hulls: analysis of randomized multivariate cubatures." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479, no. 2273 (May 2023). http://dx.doi.org/10.1098/rspa.2022.0725.
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Given a probability measure μ on a set X and a vector-valued function φ , a common problem is to construct a discrete probability measure on X such that the push-forward of these two probability measures under φ is the same. This construction is at the heart of numerical integration methods that run under various names such as quadrature, cubature or recombination. A natural approach is to sample points from μ until their convex hull of their image under φ includes the mean of φ . Here, we analyse the computational complexity of this approach when φ exhibits a graded structure by using so-called hypercontractivity. The resulting theorem not only covers the classical cubature case of multivariate polynomials, but also integration on pathspace, as well as kernel quadrature for product measures.
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Osuna, Edgar Covantes, and Dirk Sudholt. "Runtime Analysis of Restricted Tournament Selection for Bimodal Optimisation." Evolutionary Computation, April 7, 2021, 1–26. http://dx.doi.org/10.1162/evco_a_00292.
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Abstract Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel and to reduce the effect of genetic drift. We present the first rigorous runtime analyses of restricted tournament selection (RTS), embedded in a (μ+1) EA, and analyse its effectiveness at finding both optima of the bimodal function TwoMax. In RTS, an offspring competes against the closest individual, with respect to some distance measure, amongst w (window size) population members (chosen uniformly at random with replacement), to encourage competition within the same niche. We prove that RTS finds both optima on TwoMax efficiently if the window size w is large enough. However, if w is too small, RTS fails to find both optima even in exponential time, with high probability. We further consider a variant of RTS selecting individuals for the tournament without replacement. It yields a more diverse tournament and is more effective at preventing one niche from taking over the other. However, this comes at the expense of a slower progress towards optima when a niche collapses to a single individual. Our theoretical results are accompanied by experimental studies that shed light on parameters not covered by the theoretical results and support a conjectured lower runtime bound.
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Lehre, Per Kristian, and Phan Trung Hai Nguyen. "Runtime Analyses of the Population-Based Univariate Estimation of Distribution Algorithms on LeadingOnes." Algorithmica, August 28, 2021. http://dx.doi.org/10.1007/s00453-021-00862-3.
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AbstractWe perform rigorous runtime analyses for the univariate marginal distribution algorithm (UMDA) and the population-based incremental learning (PBIL) Algorithm on LeadingOnes. For the UMDA, the currently known expected runtime on the function is $${\mathcal {O}}\left( n\lambda \log \lambda +n^2\right)$$ O n λ log λ + n 2 under an offspring population size $$\lambda =\Omega (\log n)$$ λ = Ω ( log n ) and a parent population size $$\mu \le \lambda /(e(1+\delta ))$$ μ ≤ λ / ( e ( 1 + δ ) ) for any constant $$\delta >0$$ δ > 0 (Dang and Lehre, GECCO 2015). There is no lower bound on the expected runtime under the same parameter settings. It also remains unknown whether the algorithm can still optimise the LeadingOnes function within a polynomial runtime when $$\mu \ge \lambda /(e(1+\delta ))$$ μ ≥ λ / ( e ( 1 + δ ) ) . In case of the PBIL, an expected runtime of $${\mathcal {O}}(n^{2+c})$$ O ( n 2 + c ) holds for some constant $$c \in (0,1)$$ c ∈ ( 0 , 1 ) (Wu, Kolonko and Möhring, IEEE TEVC 2017). Despite being a generalisation of the UMDA, this upper bound is significantly asymptotically looser than the upper bound of $${\mathcal {O}}\left( n^2\right)$$ O n 2 of the UMDA for $$\lambda =\Omega (\log n)\cap {\mathcal {O}}\left( n/\log n\right)$$ λ = Ω ( log n ) ∩ O n / log n . Furthermore, the required population size is very large, i.e., $$\lambda =\Omega (n^{1+c})$$ λ = Ω ( n 1 + c ) . Our contributions are then threefold: (1) we show that the UMDA with $$\mu =\Omega (\log n)$$ μ = Ω ( log n ) and $$\lambda \le \mu e^{1-\varepsilon }/(1+\delta )$$ λ ≤ μ e 1 - ε / ( 1 + δ ) for any constants $$\varepsilon \in (0,1)$$ ε ∈ ( 0 , 1 ) and $$0<\delta \le e^{1-\varepsilon }-1$$ 0 < δ ≤ e 1 - ε - 1 requires an expected runtime of $$e^{\Omega (\mu )}$$ e Ω ( μ ) on LeadingOnes, (2) an upper bound of $${\mathcal {O}}\left( n\lambda \log \lambda +n^2\right)$$ O n λ log λ + n 2 is shown for the PBIL, which improves the current bound $${\mathcal {O}}\left( n^{2+c}\right)$$ O n 2 + c by a significant factor of $$\Theta (n^{c})$$ Θ ( n c ) , and (3) we for the first time consider the two algorithms on the LeadingOnes function in a noisy environment and obtain an expected runtime of $${\mathcal {O}}\left( n^2\right)$$ O n 2 for appropriate parameter settings. Our results emphasise that despite the independence assumption in the probabilistic models, the UMDA and the PBIL with fine-tuned parameter choices can still cope very well with variable interactions.
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Akhmedov, Evgeny, and Pablo Martínez-Miravé. "Solar $$ {\overline{\nu}}_e $$ flux: revisiting bounds on neutrino magnetic moments and solar magnetic field." Journal of High Energy Physics 2022, no. 10 (October 20, 2022). http://dx.doi.org/10.1007/jhep10(2022)144.
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Abstract The interaction of neutrino transition magnetic dipole moments with magnetic fields can give rise to the phenomenon of neutrino spin-flavour precession (SFP). For Majorana neutrinos, the combined action of SFP of solar neutrinos and flavour oscillations would manifest itself as a small, yet potentially detectable, flux of electron antineutrinos coming from the Sun. Non-observation of such a flux constrains the product of the neutrino magnetic moment μ and the strength of the solar magnetic field B. We derive a simple analytical expression for the expected $$ {\overline{\nu}}_e $$ ν ¯ e appearance probability in the three-flavour framework and we use it to revisit the existing experimental bounds on μB. A full numerical calculation has also been performed to check the validity of the analytical result. We also present our numerical results in energy-binned form, convenient for analyses of the data of the current and future experiments searching for the solar $$ {\overline{\nu}}_e $$ ν ¯ e flux. In addition, we give a comprehensive compilation of other existing limits on neutrino magnetic moments and of the expressions for the probed effective magnetic moments in terms of the fundamental neutrino magnetic moments and leptonic mixing parameters.
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Moss, Laurence, Hemme Hijma, Mark Demitrack, Jessica Kim, Geert Jan Groeneveld, Monique van Velzen, Marieke Niesters, Erik Olofsen, and Albert Dahan. "Neurocognitive effect of biased µ-opioid receptor agonist oliceridine, a utility function analysis and comparison with morphine." Anesthesiology, September 1, 2023. http://dx.doi.org/10.1097/aln.0000000000004758.
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Background Oliceridine (Olinvyk®) is a μ-opioid receptor agonist that in contrast to conventional opioids preferentially engages the G-protein-coupled signaling pathway. We determined the utility function of oliceridine versus morphine based on neurocognitive tests and cold pressor test. Methods The study had a randomized, double-blind, placebo-controlled, partial block 3-way crossover design. Experiments were performed in 20 male and female volunteers. Subjects received intravenous oliceridine (1 or 3 mg; cohorts of 10 subjects/dose), morphine (5 or 10 mg; cohorts of 10 subjects/dose) or placebo on three separate occasions. Prior to and following dosing, neurocognitive tests, cold pressor test and plasma drug concentrations were obtained at regular intervals. Population pharmacokinetic-pharmacodynamic analyses served as basis for construction of a utility function, which is an objective function of probability of benefit minus probability of harm. Antinociception served as measure of benefit, slowing of saccadic peak velocity and increased body sway as measures of neurocognitive harm. Results The oliceridine and morphine C50’s, i.e. the effect-site concentrations causing 50% effect, were: antinociception 13±2 and 23±7 ng/mL, saccadic peak velocity 90±14 and 54±15 ng/mL, and body sway 10±2 and 5.6±0.8 ng/mL, respectively. The ratio oliceridine/morphine of the therapeutic indices, C50(benefit)/C50(harm), were 0.34 (95% CI 0.17-0.7; p<0.01) for saccadic peak velocity and 0.33 (0.16-0.50; p<0.01) for body sway. The oliceridine utility was positive across the effect-site concentration 5-77 ng/mL, indicative of a greater probability of benefit than harm. The morphine utility was not significantly different from zero from 0-100 ng/mL. Over the concentration range 15-50 ng/mL the oliceridine utility was superior to that of morphine (p < 0.01). Similar observations were made for body sway. Conclusions These data indicate that over the clinical concentration range, oliceridine is an analgesic with a favorable safety profile over morphine when considering analgesia and neurocognitive function.
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Long, Yuqing, Yanguang Chen, and Yajing Li. "Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland." Humanities and Social Sciences Communications 10, no. 1 (October 3, 2023). http://dx.doi.org/10.1057/s41599-023-02130-x.
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AbstractRevealing spatio-temporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (μ-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q«0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seems to be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion.