Estimating area-level variation in SARS-CoV-2 infection fatality ratios

BackgroundDuring a pandemic, estimates of geographic variability in disease burden are important but limited by the availability and quality of data.MethodsWe propose a framework for estimating geographic variability in testing effort, total number of infections, and infection fatality ratio (IFR). Because symptomatic people are more likely to seek testing, we use a noncentral hypergeometric model that accounts for differential probability of positive tests. We apply this framework to the United States (U.S.) COVID-19 pandemic to estimate county-level SARS-CoV-2 IFRs from March 1, 2020 to October 31, 2020. Using data on population size, number of observed cases, number of reported deaths in each U.S. county and state, and number of tests in each U.S. state, we develop a series of estimators to identify the number of SARS-CoV-2 infections and IFRs at the county level. We then perform a simulation and compare the estimated values to simulated values to demonstrate the validity of our approach.FindingsApplying the county-level estimators to the real, unsimulated COVID-19 data spanning March 1, 2020 to October 31, 2020 from across the U.S., we found that IFRs varied from 0 to 0.0273, with an interquartile range of 0.0022 and a median of 0.0018. The estimators for IFRs, number of infections, and number of tests showed high accuracy and precision; for instance, when applied to simulated validation data sets, across counties, Pearson correlation coefficients between estimator means and true values were 0.88, 0.95, and 0.74, respectively.InterpretationWe propose an estimation framework that can be used to identify area-level variation in IFRs and performs well to estimate county-level IFRs in the U.S. COVID-19 pandemic.

Resonant Effect of High-Energy Electron–Positron Pairs Production in Collision of Ultrarelativistic Electrons with an X-ray Electromagnetic Wave

The process of resonant high-energy electron–positron pairs production by electrons in an X-ray pulsar electromagnetic field is studied theoretically. Under the resonance conditions, the second-order process under consideration effectively reduces into two sequential first-order processes: X-ray-stimulated Compton effect and X-ray–stimulated Breit–Wheeler process. The kinematics of the process is studied in detail: the dependencies of the energy of the scattered electron on its outgoing angle and the energies of the particles of the pair on the outgoing angle of the scattered electron and the opening angle of the pair are obtained. The analysis of the number of different possible particles energies values in the entire range of the angles is also carried out, according to which the energies of the particles of the pair can take up to eight different values at a fixed outgoing angle of the scattered electron and opening angle of the pair. The estimate of the resonant differential probability per unit time of the process, which reaches the maximum value of 24 orders of the value of the non-resonant differential probability per unit time, is obtained. The angular distribution of the differential probability per unit time of the process is analyzed, particularly for the case of high-energy positrons presenting in pulsar radiation.

Maximums of the Additive Differential Probability of Exclusive-Or

At FSE 2004, Lipmaa et al. studied the additive differential probability adp⊕(α,β → γ) of exclusive-or where differences α,β,γ ∈ Fn2 are expressed using addition modulo 2n. This probability is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as the increasingly popular Addition-Rotation-XOR (ARX) constructions. The focus of this paper is on maximal differentials, which are helpful when constructing differential trails. We provide the missing proof for Theorem 3 of the FSE 2004 paper, which states that maxα,βadp⊕(α,β → γ) = adp⊕(0,γ → γ) for all γ. Furthermore, we prove that there always exist either two or eight distinct pairs α,β such that adp⊕( α,β → γ) = adp⊕(0,γ → γ), and we obtain recurrence formulas for calculating adp⊕. To gain insight into the range of possible differential probabilities, we also study other properties such as the minimum value of adp⊕(0,γ → γ), and we find all γ that satisfy this minimum value.

Accelerating the Search of Differential and Linear Characteristics with the SAT Method

The introduction of the automatic search boosts the cryptanalysis of symmetric-key primitives to some degree. However, the performance of the automatic search is not always satisfactory for the search of long trails or ciphers with large state sizes. Compared with the extensive attention on the enhancement for the search with the mixed integer linear programming (MILP) method, few works care for the acceleration of the automatic search with the Boolean satisfiability problem (SAT) or satisfiability modulo theories (SMT) method. This paper intends to fill this vacancy. Firstly, with the additional encoding variables of the sequential counter circuit for the original objective function in the standard SAT method, we put forward a new encoding method to convert the Matsui’s bounding conditions into Boolean formulas. This approach does not rely on new auxiliary variables and significantly reduces the consumption of clauses for integrating multiple bounding conditions into one SAT problem. Then, we evaluate the accelerating effect of the novel encoding method under different sets of bounding conditions. With the observations and experience in the tests, a strategy on how to create the sets of bounding conditions that probably achieve extraordinary advances is proposed. The new idea is applied to search for optimal differential and linear characteristics for multiple ciphers. For PRESENT, GIFT-64, RECTANGLE, LBlock, TWINE, and some versions in SIMON and SPECK families of block ciphers, we obtain the complete bounds (full rounds) on the number of active S-boxes, the differential probability, as well as the linear bias. The acceleration method is also employed to speed up the search of related-key differential trails for GIFT-64. Based on the newly identified 18-round distinguisher with probability 2−58, we launch a 26-round key-recovery attack with 260.96 chosen plaintexts. To our knowledge, this is the longest attack on GIFT-64. Lastly, we note that the attack result is far from threatening the security of GIFT-64 since the designers recommended users to double the number of rounds under the related-key attack setting.

Aftershock Rate Changes at Different Ocean Tide Heights

The differential probability gain approach is used to estimate quantitatively the change in aftershock rate at various levels of ocean tides relative to the average rate model. An aftershock sequences are analyzed from two regions with high ocean tides, Kamchatka and New Zealand. The Omori-Utsu law is used to model the decay over time, hypothesizing an invariable spatial distribution. Ocean tide heights are considered rather than phases. A total of 16 sequences of M ≥6 aftershocks off Kamchatka and 15 sequences of M ≥6 aftershocks off New Zealand are examined. The heights of the ocean tides at various locations were modeled using FES 2004. Vertical stress changes due to ocean tides are here about 10–20 kPa, that is, at least several times greater than the effect due to Earth tides. An increase in aftershock rate is observed by more than two times at high water after main M ≥6 shocks in Kamchatka, with slightly less pronounced effect for the earthquakes of M = 7.8, December 15, 1971 and M = 7.8, December 5, 1997. For those two earthquakes, the maximum of the differential probability gain function is also observed at low water. For New Zealand, we also observed an increase in aftershock rate at high water after thrust type main shocks with M ≥6. After normal-faulting main shocks there was the tendency of the rate increasing at low water. For the aftershocks of the strike-slip main shocks we observed a less evident impact of the ocean tides on their rate. This suggests two main mechanisms of the impact of ocean tides on seismicity rate, an increase in pore pressure at high water, or a decrease in normal stress at low water, both resulting in a decrease of the effective friction in the fault zone.

Criminal Justice Involvement, Transition to Fatherhood, and the Demographic Foundation of the Intergenerational Transmission of Crime

Most analyses of the intergenerational transmission of criminal justice contacts compare outcomes of the second generation to the criminal history of the first generation. Such analyses ignore potential differential fertility and family formation processes and exclude childless individuals. Ignoring the demographic process underlying transmission introduces selection bias into estimates of the intergenerational transmission of criminal justice contacts insofar as the first generation’s criminal history affects family formation and the probability of parenthood. In this study, we use a cohort of all Danish men born 1965-1973 including complete fertility information and criminal justice history to account for bias caused by differential selection into fatherhood across criminal histories. We demonstrate that seriousness of criminal justice involvement is associated with earlier transition to fatherhood but ultimately higher levels of childlessness. Criminal activity prior to the onset of transition to fatherhood predicts ultimate childlessness. Conditioned on becoming a father, men with criminal justice histories have a similar number of children as men without a history of criminal justice contacts. Ultimately, the findings suggest that existing estimates of the intergenerational transmission of criminal justice contacts are overestimated when considered at the population level due to differential probability of ever becoming a father.

A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field

Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cryptographically strong 8×8 S-boxes by applying an adjacency matrix on the Galois field GF(28). The adjacency matrix is obtained corresponding to the coset diagram for the action of modular group PSL(2,Z) on a projective line PL(F7) over a finite field F7. The strength of the proposed S-boxes is examined by common S-box tests, which validate their cryptographic strength. Moreover, we use the majority logic criterion to establish an image encryption application for the proposed S-boxes. The encryption results reveal the robustness and effectiveness of the proposed S-box design in image encryption applications.

Resonant Effect for Breit–Wheeler Process in the Field of an X-ray Pulsar

The resonant process of the creation of an ultrarelativistic electron–positron pair by two hard gamma quanta in the field of an X-ray pulsar (the Breit–Wheeler process modified by an external field) was theoretically studied. Under resonance conditions, the intermediate virtual electron (positron) in the external field becomes a real particle. As a result, there are four reaction channels for the process instead of two. For each of those channels, the initial process of the second order in the fine structure constant in the field of an X-ray pulsar effectively reduces into two successive processes of the first order: X-ray-stimulated Breit–Wheeler process and X-ray-stimulated Compton effect. The resonant kinematics of the process was also studied in detail. The process had characteristic threshold energy, and all initial and final particles had to be ultrarelativistic and propagate in a narrow cone. Furthermore, the resonant energy spectrum of the electron-positron pair significantly depended on emission angles. Clearly, there was a qualitative difference between resonant and nonresonant cases. Lastly, the resonant differential probability of studied process was obtained. The resonant differential probability significantly exceeded the nonresonant one without the external field of an X-ray pulsar.

Resonant Ultrarelativistic Electron–Positron Pair Production by High-Energy Electrons in the Field of an X-ray Pulsar

The process of resonant high-energy electron–positron pair production by an ultrarelativistic electron colliding with the field of an X-ray pulsar is theoretically investigated. Resonant kinematics of the process is studied in detail. Under the resonance condition, the intermediate virtual photon in the X-ray pulsar field becomes a real particle. As a result, the initial process of the second order in the fine structure constant effectively reduces into two successive processes of the first order: X-ray-stimulated Compton effect and X-ray-stimulated Breit–Wheeler process. For a high-energy initial electron all the final ultrarelativistic particles propagate in a narrow cone along the direction of the initial electron momentum. The presence of threshold energy for the initial electron which is of order of 100 MeV for 1-KeV-frequency field is shown. At the same time, the energy spectrum of the final particles (two electrons and a positron) highly depends on their exit angles and on the initial electron energy. This result significantly distinguishes the resonant process from the non-resonant one. It is shown that the resonant differential probability significantly exceeds the non-resonant one.

Parallel multi-layer selector S-Box based on lorenz chaotic system with FPGA implementation

<p><span>The substitution box (S-Box) is the main block in the encryption system, which replaces the non-encrypted data by dynamic secure and hidden data. S-Box can be designed based on complex nonlinear chaotic systems that presented in recent papers as a chaotic S-Box. The hardware implementation of these chaotic systems suffers from long processing time (low speed), and high-power consumption since it requires a large number of non-linear computational models. In this paper, we present a high-speed FPGA implementation of Parallel Multi-Layer Selector Substitution Boxes based on the Lorenz Chaotic System (PMLS S-Box). The proposed PMLS chaotic S-Box is modeled using Xilinx System Generator (XSG) in 32 bits fixed-point format, and the architecture implemented into Xilinx Spartan-6 X6SLX45 board. The maximum frequency of the proposed PMLS chaotic S-Box is 381.764 MHz, with dissipates of 77 mwatt. Compared to other S-Box chaotic systems, the proposed one achieves a higher frequency and lower power consumption. In addition, the proposed PMLS chaotic S-Box is analyzed based on S-Box standard tests such as; Bijectivity property, nonlinearity, strict avalanche criterion, differential probability, and bits independent criterion. The five different standard results for the proposed S-Box indicate that PMLSC can effectively resist crypto-analysis attacks, and is suitable for secure communications.</span></p>