Search Results (10)

Modeling efforts are needed to predict trends in COVID-19 cases and related health outcomes, aiding in the development of management strategies and adaptation measures. This study was conducted to assess whether the SARS-CoV-2 viral load in wastewater could serve as a predictor for forecasting COVID-19 cases, hospitalizations, and deaths using copula-based time series modeling. SARS-CoV-2 RNA load in wastewater in Chesapeake, VA, was measured using the RT-qPCR method. A Gaussian copula time series (CTS) marginal regression model, incorporating an autoregressive moving average model and Gaussian copula function, was used as a forecasting model. Wastewater SARS-CoV-2 viral loads were correlated with COVID-19 cases. The forecasted model with both Poisson and negative binomial marginal distributions yielded trends in COVID-19 cases that closely paralleled the reported cases, with 90% of the forecasted COVID-19 cases falling within the 99% confidence interval of the reported data. However, the model did not effectively forecast the trends and the rising cases of hospital admissions and deaths. The forecasting model was validated for predicting clinical cases and trends with a non-normal distribution in a time series manner. Additionally, the model showed potential for using wastewater SARS-CoV-2 viral load as a predictor for forecasting COVID-19 cases. Full article

A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) function. Also, it is shown that the convolution of power series q-distributions is also a power series q-distribution. Furthermore, the q-Poisson (Heine and Euler), q-binomial of the first kind, negative q-binomial of the second kind, and q-logarithmic distributions are shown to be members of this class of distributions and their q-factorial moments are deduced. In addition, the convolution properties of these distributions are examined. Full article

The 22q11.2 deletion syndrome (22q11.2DS) manifests as a wide range of medical conditions across a number of systems. Pediatric growth deficiency with some catch-up growth is reported, but there are few studies of final adult height. We aimed to investigate how final adult height in 22q11.2DS compared with general population norms, and to examine predictors of short stature in in a cohort of 397 adults with 22q11.2DS (aged 17.6–76.3 years) with confirmed typical 22q11.2 microdeletion (overlapping the LCR22A to LCR22B region). We defined short stature as <3rd percentile using population norms. For the subset (n = 314, 79.1%) with 22q11.2 deletion extent, we used a binomial logistic regression model to predict short stature in 22q11.2DS, accounting for effects of sex, age, ancestry, major congenital heart disease (CHD), moderate-to-severe intellectual disability (ID), and 22q11.2 deletion extent. Adult height in 22q11.2DS showed a normal distribution but with a shift to the left, compared with population norms. Those with short stature represented 22.7% of the 22q11.2DS sample, 7.6-fold greater than population expectations (p < 0.0001). In the regression model, moderate-to-severe ID, major CHD, and the common LCR22A-LCR22D (A-D) deletion were significant independent risk factors for short stature while accounting for other factors (model p = 0.0004). The results suggest that the 22q11.2 microdeletion has a significant effect on final adult height distribution, and on short stature with effects appearing to arise from reduced gene dosage involving both the proximal and distal sub-regions of the A-D region. Future studies involving larger sample sizes with proximal nested 22q11.2 deletions, longitudinal lifetime data, parental heights, and genotype data will be valuable. Full article

A new class of distribution called the Fréchet binomial (FB) distribution is proposed. The new suggested model is very flexible because its probability density function can be unimodal, decreasing and skewed to the right. Furthermore, the hazard rate function can be increasing, decreasing, up-side-down and reversed-J form. Important mixture representations of the probability density function (pdf) and cumulative distribution function (cdf) are computed. Numerous sub-models of the FB distribution are explored. Numerous statistical and mathematical features of the FB distribution such as the quantile function ($Q_{UN}F$); moments ($M_O$); incomplete $M_O$ ($I{M}_O$); conditional $M_O$ ($C{M}_O$); $M_O$ generating function ($M_{O}GF$); probability weighted $M_O$ ($PW{M}_O$); order statistics; and entropy are computed. When the life test is shortened at a certain time, acceptance sampling (ACS) plans for the new proposed distribution, FB distribution, are produced. The truncation time is supposed to be the median lifetime of the FB distribution multiplied by a set of parameters. The smallest sample size required ensures that the specified life test is obtained at a particular consumer’s risk. The numerical results for a particular consumer’s risk, FB distribution parameters and truncation time are generated. We discuss the method of maximum likelihood to estimate the model parameters. A simulation study was performed to assess the behavior of the estimates. Three real datasets are used to illustrate the importance and flexibility of the proposed model. Full article

There exists a natural trade-off in public key encryption (PKE) schemes based on ring learning with errors (RLWE), namely: we would like a wider error distribution to increase the security, but it comes at the cost of an increased decryption failure rate (DFR). A straightforward solution to this problem is the error-correcting code, which is commonly used in communication systems and already appears in some RLWE-based proposals. However, applying error-correcting codes to those cryptographic schemes is far from simply installing an add-on. Firstly, the residue error term derived by decryption has correlated coefficients, whereas most prevalent error-correcting codes with remarkable error tolerance assume the channel noise to be independent and memoryless. This explains why only simple error-correcting methods are used in existing RLWE-based PKE schemes. Secondly, the residue error term has correlated coefficients leaving accurate DFR estimation challenging even for uncoded plaintext. It can be found in the literature that a tighter DFR estimation can effectively create a DFR margin. Thirdly, most error-correcting codes are not well designed for safety considerations, e.g., syndrome decoding has a nonconstant time nature. A code good at error correcting might be weak under a variety of attacks. In this work, we propose a polar coding scheme for RLWE-based PKE. A relaxed “independence” assumption is used to derive an uncorrelated residue noise term, and a wireless communication strategy, outage, is used to construct polar codes. Furthermore, some knowledge about the residue noise is exploited to improve the decoding performance. With the parameterization of NewHope Round 2, the proposed scheme creates a considerable DRF margin, which gives a competitive security improvement compared to state-of-the-art benchmarks. Specifically, the security is improved by $28.8\%$, while a DFR of $2^{-149}$ is achieved a for code rate pf 0.25, $n=1024,q=$ 12,289, and binomial parameter $k=55$. Moreover, polar encoding and decoding have a quasilinear complexity $O\left(N{log}_{2}N\right)$ and intrinsically support constant-time implementations. Full article

The Eating Disorder Examination Interview Bariatric Surgery Version (EDE-BSV) assesses eating pathology after bariatric surgery but requires significant training and time to administer. Consequently, we developed a questionnaire format called the Eating Disorders After Bariatric Surgery Questionnaire (EDABS-Q). This study evaluates the consistency of responsiveness between the two formats. After surgery, 30 patients completed the EDE-BSV and EDABS-Q in a restricted randomized design. Patient reported behavior for each item which was converted to a score following the Eating Disorder Examination-Questionnaire (EDE-Q) scoring scheme. Responses fell into three distributions: (1) dichotomous, (2) ordinal, or (3) unimodal. Distributions of items were not different between the two formats and order did not influence response. Tests of agreement (normal approximation of the binomial test) and association (χ² analyses on binary data and spearman rank order correlations on ordinal items) were performed. Percent concordance was high across items (63–100%). Agreement was significant in 31 of 41 items (Bonferroni-P < 0.001). Association was significant in 10 of 21 in χ²–appropriate items (Bonferroni-P < 0.002), and the ordinal items had highly significant correlations between formats (Bonferroni-P < 0.0125). The EDABS-Q is an adequate substitute for the EDE-BSV and may be useful for research and clinical evaluation of eating pathology after bariatric surgery. Full article

This work analyzes the relationship between crash frequency N (crashes per hour) and exposure Q (cars per hour) on the macroscopic level of a whole city. As exposure, the traffic flow is used here. Therefore, it analyzes a large crash database of the city of Berlin, Germany, together with a novel traffic flow database. Both data display a strong weekly pattern, and, if taken together, show that the relationship $N\left(Q\right)$ is not a linear one. When Q is small, N grows like a second-order polynomial, while at large Q there is a tendency towards saturation, leading to an S-shaped relationship. Although visible in all data from all crashes, the data for the severe crashes display a less prominent saturation. As a by-product, the analysis performed here also demonstrates that the crash frequencies follow a negative binomial distribution, where both parameters of the distribution depend on the hour of the week, and, presumably, on the traffic state in this hour. The work presented in this paper aims at giving the reader a better understanding on how crash rates depend on exposure. Full article

Non-orthogonal multiple access (NOMA) is the technique proposed for multiple access in the fifth generation (5G) cellular network. In NOMA, different users are allocated different power levels and are served using the same time/frequency resource blocks (RBs). The main challenges in existing NOMA systems are the limited channel feedback and the difficulty of merging it with advanced adaptive coding and modulation schemes. Unlike formerly proposed solutions, in this paper, we propose an effective channel estimation (CE) algorithm based on the long-short term memory (LSTM) neural network. The LSTM has the advantage of adapting dynamically to the behavior of the fluctuating channel state. On average, the use of LSTM results in a 10% lower outage probability and a 37% increase in the user sum rate as well as a maximal reduction in the bit error rate (BER) of 50% in comparison to the conventional NOMA system. Furthermore, we propose a novel power coefficient allocation algorithm based on binomial distribution and Pascal’s triangle. This algorithm is used to divide power among N users according to each user’s channel condition. In addition, we introduce adaptive code rates and rotated constellations with cyclic Q-delay in the quadri-phase shift keying (QPSK) and quadrature amplitude modulation (QAM) modulators. This modified modulation scheme overcomes channel fading effects and helps to restore the transmitted sequences with fewer errors. In addition to the initial LSTM stage, the added adaptive coding and modulation stages result in a 73% improvement in the BER in comparison to the conventional NOMA system. Full article

Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Rényi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula. Full article

From Kemp [1], we have a family of confluent q-Chu- Vandermonde distributions, consisted by three members I, II and III, interpreted as a family of q-steady-state distributions from Markov chains. In this article, we provide the moments of the distributions of this family and we establish a continuous limiting behavior for the members I and II, in the sense of pointwise convergence, by applying a q-analogue of the usual Stirling asymptotic formula for the factorial number of order n. Specifically, we initially give the q-factorial moments and the usual moments for the family of confluent q-Chu- Vandermonde distributions and then we designate as a main theorem the conditions under which the confluent q-Chu-Vandermonde distributions I and II converge to a continuous Stieltjes-Wigert distribution. For the member III we give a continuous analogue. Moreover, as applications of this study we present a modified q-Bessel distribution, a generalized q-negative Binomial distribution and a generalized over/underdispersed (O/U) distribution. Note that in this article we prove the convergence of a family of discrete distributions to a continuous distribution which is not of a Gaussian type. Full article