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This paper explores the least absolute deviation (LAD) estimator of the autoregressive model with heavy-tailed G-GARCH(1, 1) noise. When the tail index α ∈ ( 1 , 2 ] , it is shown that the LAD estimator asymptotically converges to a linear function of a series of α -stable random vectors with a rate of convergence n 1 − 1 ∕ α . The result is significantly different from that of the corresponding least square estimator which is not consistent, and partially solves the problem on the asymptoticity of the LAD estimator when the tail index is less than 2. A simulation study is carried out to assess the performance of the LAD estimator and a real example is given to illustrate this approach.

An oblivious linear function evaluation protocol, or OLE, is a two-party protocol for the function f ( x ) = a x + b, where a sender inputs the field elements a, b, and a receiver inputs x and learns f ( x ). OLE can be used to build secret-shared multiplication, and is an essential component of many secure computation applications including general-purpose multi-party computation, private set intersection and more. In this work, we present several efficient OLE protocols from the ring learning with errors (RLWE) assumption. Technically, we build two new passively secure protocols, which build upon recent advances in homomorphic secret sharing from (R)LWE (Boyle et al. in: EUROCRYPT 2019, Part II (2019) 3–33 Springer), with optimizations tailored to the setting of OLE. We upgrade these to active security using efficient amortized zero-knowledge techniques for lattice relations (Baum et al. in: CRYPTO 2018, Part II (2018) 669–699 Springer), and design new variants of zero-knowledge arguments that are necessary for some of our constructions. Our protocols offer several advantages over existing constructions. Firstly, they have the lowest communication complexity amongst previous, practical protocols from RLWE and other assumptions; secondly, they are conceptually very simple, and have just one round of interaction for the case of OLE where b is randomly chosen. We demonstrate this with an implementation of one of our passively secure protocols, which can perform more than 1 million OLEs per second over the ring Z m , for a 120-bit modulus m, on standard hardware.

The moving asymptotes function is widely applied as sequential explicit convex approximation in topology optimization, due to the controllable conservatism and convergence. In virtue of these advantages, it is supposed that the efficiency of optimality criteria method will become higher if constraint functions are approximated by moving asymptotes function instead of linear function. This work presents an optimality criteria method for topology optimization under multiple constraints where the constraint functions are approximated by moving asymptotes function. The dual feasibility condition is customarily adopted to establish explicit update scheme of topological variable, where hypothesis of active topological variable set is avoided, in the case that gradient of objective function is positive. The complementary slackness condition and primal feasibility condition are combined into a simplified dual programming to solve for the Lagrange multipliers, where hypothesis of active constraint set is avoided. Three benchmark examples under multiple displacement, stress, compliance or eigenfrequency constraints are solved by the presented optimality criteria method, the results are compared to the method of moving asymptotes and the optimality criteria method with linear constraint approximation.

In this paper, in the scope of a non-extensive statistical model for the nucleon’s structure function, the volume of the gluons in the nucleons and the relations among the temperature, T, the parameter “q” of Tsallis statistics, and the scattering energies, Q2, are studied. A system of equations with the usual sum rules are solved for the valence quarks, the experimental results for the polarized structure function, and the estimated carried moments for gluons and quarks. Each state of T and q leads to a set of chemical potentials and different radii for gluons and quarks. We conclude that gluons must occupy a larger volume than the quarks to fit the fraction of the total momentum. A linear function of the temperature with Q2 is obtained as an approach. The obtained range of temperatures is different from the previous models.

The speed of short-term memory scanning is thought to be captured in the slope of the linear function of mean reaction times (RTs) regressed on set size in the Sternberg memory scanning task (SMST). Individual differences in the slope parameter have been hypothesized to correlate with general intelligence ('g'). However, this correlation can usually not be found. This present study chose a fixed-links model (FLM) approach to re-evaluate the RT slope parameter on a latent level in a sample of 102 participants aged 18 to 61 years who completed the SMST with set sizes 1, 3, and 5. The same was tried for P3 latencies to investigate whether or not both parameters measure the same cognitive processes in the SMST, and to assess the usability of both slopes to predict 'g'. For RTs, a linear increase with set size was found. The slope of mean RTs correlated with 'g' on a manifest level already. The FLM approach could better reveal this relationship with the correlation between the slope and 'g' being substantially higher. For P3 latencies, we found no evidence for a linear increase, but a general increase from the smallest set size to the two larger ones. This indicates that RTs and P3 latencies do not measure the same cognitive processes in the SMST. The FLM proved suitable to investigate the association between the speed of short-term memory scanning and intelligence.

BACKGROUNDAn altered balance of neuronal excitation and inhibition (E-I balance) might be implicated in the co-occurrence of autism and intellectual disability, but this hypothesis has never been tested. E-I balance changes can be estimated from the spectral slope of the aperiodic 1/f neural activity. Herein, we used magnetoencephalography (MEG) to test whether the 1/f slope would differentiate ASD children with and without intellectual disability.METHODSMEG was recorded at rest with eyes open/closed in 49 boys with ASD aged 6-15 years with a broad range of IQs, and in 49 age-matched typically developing (TD) boys. The cortical source activity was estimated using the LCMV beamformer approach. We then extracted the 1/f slope by fitting a linear function in to the log-log-scale power spectra in the high-frequency range.RESULTSThe grand averaged 1/f slope was steeper in the eyes closed than in the eyes open condition, but had high rank-order stability between them. In line with the previous research, the slope flattened with age. Children with ASD and below-average (CONCLUSIONSThe atypically flattened spectral slope of aperiodic activity in children with ASD and below-average IQ suggests a shift of the global E-I balance toward hyper-excitation. The spectral slope can provide an accessible non-invasive biomarker of the E-I ratio for translational research and making objective judgments about treatment effectiveness.

The retino-cortical visual pathway is retinotopically organized: Neighborhood relationships on the retina are preserved in the mapping to the cortex. Size relationships in that mapping are also highly regular: The size of a patch in the visual field that maps onto a cortical patch of fixed size, follows, along any radius and in a wide range, simply a linear function with retinal eccentricity. This is referred to as M-scaling . As a consequence, and under simplifying assumptions, the mapping of retinal to cortical location follows a logarithmic function along a radius, as was already shown by Fischer (1973) and Schwartz (1977, 1980). The M -scaling function has been determined for many visual tasks. It is standardly characterized by its foveal threshold value, together with the eccentricity where that value doubles, called E 2 . The cortical location function, on the other hand, is commonly specified by parameters that are separately determined from the empirical findings. Here, the psychophysical and neuroscience traditions are brought together by specifying the cortical equations in terms of the parameters customary in psychophysics. The equations go beyond those published in the past in being more explicit and ready for application, and they allow easy switching between M -scaling and cortical mapping. A new parameter, d 2 , is proposed to describe the cortical map, as a cortical counterpart to E 2 and typical values for it are given. The resulting cortical-location function is then applied to data from a number of fMRI studies. One pitfall is discussed and spelt out as a set of equations, namely the common myth that a pure logarithmic function will give an adequate map: The popular omission of a constant term renders the equations ill-defined in and around the retinotopic center. The correct equations are finally extended to describe the cortical map of Bouma’s law on visual crowding. The result contradicts recent suggestions that critical crowding distance corresponds to constant cortical distance.

The Holt–Klee theorem says that the graph of a d -polytope, with edges oriented by a linear function on P that is not constant on any edge, admits d independent monotone paths from the source to the sink. We prove that the digraphs obtained from oriented matroid programs of rank d + 1 on n + 2 elements, which include those from d -polytopes with n facets, admit d independent monotone paths from source to sink if d ≤ 4 . This was previously only known to hold for d ≤ 3 and n ≤ 6 .

Volt-Amp profiles are used to describe electrodialysis (ED) dynamics when the concentration of the diluate is equal to the concentration of the concentrate and both are at high concentration. A standard electronic model that treats the ED process as a series of resistors failed to describe the performance of a 10-cell pair, 200 cm2 per membrane pilot electrodialysis unit treating 0.5–6% NaCl. The standard electronic model resulted in a regression coefficient of R2 0.999. The current was plotted as a function of the conductivity of the salt at a constant conductivity of electrode rinse solution. Each curve was a function of the applied voltage. The value of the saturation coefficient for the system plots as {Dsat } ∼ 22.1 mS/cm (2.21 S/m). The kinetic coefficient iMAX plotted as a linear function of the effective voltage at 25 °C (298°K). More importantly, a series of tests with a constant feed conductivity and with varied electrode rinse solution conductivity also plotted as Michaelis-Menten type curves. The saturation coefficient for the electrode rinse solution also fitted well to {Esat } ∼ 22.1 mS/cm (2.21 S/m) and the values for i MAX were also linear with respect to applied voltage. Overall, the results from 12 data sets follow the formula i = αβi MAX where α and β are the ratios of the conductivity of the fluid divided by the sum of the conductivity plus the saturation, e.g., for electrode rinse solution α = {E}/({E} + {Esat}) and for the electrode rinse β = {D}/({D} + {Dsat}), indicating the co-dependence of the feedstock and electrode rinse in the overall process dynamics. This interpretation is in opposition to the standard modeling of ED where the process is viewed as a series of resistances and the electrode rinse resistance is usually determined to be negligible. These data suggest that the effects of saturated feedstock and saturated rinse solution, measured as current or ion transport, are inextricably co-dependent. Three full-batch test runs of between 7.2 and 9-hr duration using different initial feedstock and electrode rinse water conditions were analyzed to estimate the relative effects of diluate and concentrate concentration on the test results. A third saturation coefficient was introduced, γ = {C}/({C} + {Csat}) where the terms {C} and {C sat } represent the conductivity and the saturation coefficient of the concentrate. The model for long duration batch tests, including the different effects of the concentrate and diluate, is well represented by i = (αβ0.8 γ 0.2 i MAX). The empirical power coefficients, β0.8 and γ0.2, indicate that the diluate conductivity carries more influence on the rate of the process than does the conductivity of the concentrate. The model has the potential to allow for the scale-up of the ED process using at most one adjustable parameter (the saturation coefficient of the membrane measured as mS/cm or S/cm). Michaelis-Menten kinetics and the modifications by others represent a rich literature on the modeling of different types of inhibition, topics of concern for membrane transport phenomenon.

The pressure drop (dP) and apparent viscosity characterize the ability of foam to control gas mobility in core flooding experiments. There is no clarity regarding which factor, total flow rate (qt), foam quality (fg), gas (qg) or liquid (ql) flow rate, determines the dP. The inconsistency in interpretation can be caused by the differences in conditions of experiments, which are carried out at one fixed and other varying parameter. In this study, dP and length of foam drops at the outlet are measured in three types of experiments at 400 and 500 psi for comparison: 1) scans at fixed total flow rate and varying fg; 2) tests at fixed liquid flow rate and varying gas flow rates; 3) tests at fixed gas flow rate and varying liquid flow rates. In foam scans 1, the dP measured at two qt decreased almost linearly due to low foamability starting at fg = 0.3, indicating a high quality regime. The length of foam drops and the bubble size increased with the increase in fg. In tests 2 and 3, there was no direct relationship between dP and qg at a constant ql, but dP increased with increasing ql at constant qg, which is in line with other publications. In addition, there was no direct dependence of the foam texture on the increase in qg and ql. The discrepancy in the dependence of dP on ql and qg between the three experiments was due to the fact that different combinations of ql and qg used in tests 2 and 3 resulted in the same fg and qt, which led to data overlap and data distribution in both high and low regimes. Meanwhile, dP measured in all three experiments was a linear function of the liquid flow rate with a line slope equal to the outlet pressure, regardless of the total flow rate. Due to the mathematical expression, the equation dP = P · ql can be called the equation of ideal foam and used as a test case for further comparisons. Thus, ql is the governing factor in high quality regime for a given surfactant and conditions. The slopes were also equal to the outlet pressures for the dP curves as a function of qt in tests 2 and 3. Irrespective the linear correlation between dP and ql, the deviations were observed at medium values of foam quality at 400 psi. These deviations were accompanied by the simultaneous deviations in the length of foam drops, showing that they were of nonrandom nature. In some deviating points, the foam texture at the outlet changed abruptly and disproportionately to fg changes. This could be the evidence of the intermediate state between the coarse-foam and strong-foam.

Spectra and emission efficiencies of x-rays produced by hot electrons (hot-e’s) with drift Maxwellian distribution are studied using both analytical and numerical methods. The analytic expressions are particularly useful for the analysis of x-ray spectra produced by hot-e’s in laser-produced plasma. Both analytical and numerical results show that when hot-e’s have a nonzero drift velocity, the bremsstrahlung spectrum is still approximately a linear function in logarithmic coordinates, which indicates that the process of inferring hot-e’s temperature from the slope of x-ray spectrum needs to be revisited under certain circumstances.

The decay processes of wave-packets scattered by periodically perturbed and unperturbed rounded-rectangular potentials are studied numerically and theoretically, when the widths of the potentials L are very large. For the case of the unperturbed potentials, four different stages successively arise in the decay process of the wave in the potential region: two pre-exponential decays, namely power–law decay of t −3 and oscillating power–law decay, exponential decay and post-exponential decay, which is also power–law decay of t −3. The post-exponential decay is usually extremely small in magnitude. The characteristics of the pre-exponential and exponential decays are explained with the properties of resonance states, i.e. the Gamow states, for the unperturbed system. The rate of the exponential decay is determined by the imaginary part of the eigenenergy of the first resonance state. For the two pre-exponential decays, the ending time of the t −3 decay is a linear function of L and that of the oscillating power-law decay is proportional to L 3. In the limit of L → ∞, the t −3 decay is observed persistently, namely the decay for the rounded-step potential. For the perturbed potentials, even if the average energy of an initial wave-packet is relatively smaller than the oscillating potential, the noninstanton tunnelling, i.e. the multi-quanta absorption tunnelling, raises the tunnelling wave component up to the oscillating top of the rounded-rectangular potential, and the tunnelling probability rapidly increases with the perturbation strength. The properties of the resonance states are almost the same as those of the Gamow states because of the flatness of the potential top. As a result, the decay process after the tunnelling is almost the same as that for the unperturbed system. It is suggested that the tunnelling amplitude and tunnelling time, namely the amplitude and period of the pre-exponential decay, can be controlled by the perturbation strength and the potential width, respectively.

Our present work is devoted to investigate the existence of a compact stellar configuration model in the framework of f ( R , T ) gravity theory, where R and T denote the Ricci scalar and trace of energy–momentum tensor, respectively. Here, we have developed a setup using a well-known Karmarkar condition and obtained a well-behaved embedding class-one solution with specific linear function f ( R , T ) = R + 2 χ T , where χ is the coupling constant. We obtain a specific form of differential equation by using this condition that showed a connection between e λ and e ν . With the viability of our stellar model, we have checked all the physical parameters such as density, pressure, speed of sound, TOV equation, redshift, etc. of compact stars like RX J1856-37,4U1538-52, SAX J1808.4-3658, EXO 1785-248, PSR J1903+327, and Vela X-1 which are conferred in tables and graphs. And the observation suggested, our solution for compact stars using Karmarkar condition in the background of f ( R , T ) has shown more consistency and the results are fair and appealing.