Logarithmic Scale Research Articles

Is the approximate number system capacity limited? Extended display duration does not increase the limits of linear number estimation.

The approximate number system (ANS) is widely regarded as handling numbers beyond the subitizing range. However, a review of a variety of historical data suggests there is a sharp break in the estimation of visuospatial number at about 20 items. Estimates below 20 tend to be unbiased. Those above 20 tend to show underestimation that can be well-fit by a power function with an exponent less than one. Here we manipulate display duration between subjects to confirm that this break is not simply an artifact of brief displays, but seems to reflect a shift in perceptual magnitude estimation from an ANS (unbiased estimation) to a correlated numerosity system (with log scaling). Detailed analysis of both response time and variability suggests that the sharp break at 20 observed here may reflect a capacity limitation in a linear accumulator system, which gives way to alternative magnitude information beyond 20. Implications for studies of number comparison and math performance are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Agreement and reliability of hepatic transient elastography in patients with chronic hepatitis C: Across-sectional test-retest study.

Transient elastography (TE) has largely replaced liver biopsy to evaluate fibrosis stage and cirrhosis in chronic hepatitis C. Previous studies have reported excellent reliability of TE but agreement metrics have not been reported. This study aimed to assess interrater agreement and reliability of repeated TE measurements. Two operators performed TE independently, directly after each other. The primary outcome was disagreement, defined as a difference in TE results between operators of ≥33%, as well as the smallest detectable change, SDC95 (i.e., the difference between measurements needed to state with 95% certainty that there is a difference in underlying stiffness). Secondary outcomes included reliability, measured as intraclass correlation (ICC), and patient and examination characteristics associated with the agreement. In total, 65 patients were included, with a mean liver stiffness of 9.7 kPa. Of these, 21 (32%) had a disagreement in TE results of ≥33% between the two operators. The SDC95 on the log scale was 1.97, indicating that an almost twofold increase or decrease in liver stiffness would be required to confidently represent a change in the underlying fibrosis. Reliability, estimated using the ICC, was acceptable at 0.86. In a post hoc analysis, fasting less than 5 h before TE was associated with a higher degree of disagreement (48% vs. 19%, p = 0.03). In our clinical setting, interrater agreement in directly repeated TE measurements was surprisingly low. It is essential to further investigate the reliability and agreement of TE to determine its validity and usefulness.

Vagus Nerve Stimulation Paired With Upper-Limb Rehabilitation After Stroke: 2- and 3-Year Follow-up From the Pilot Study

ObjectiveTo assess whether a long-term home-based intervention using Paired VNS therapy is feasible and whether the benefits of Paired VNS therapy are maintained beyond 1 year. DesignA long-term follow-up study. SettingThree centers in the United States and 1 in the United Kingdom. ParticipantsAdults with chronic ischemic stroke (n=15) with moderate to severe arm and hand impairment. InterventionsParticipants were implanted with a VNS device followed by 6 weeks of in-clinic therapy with Paired (Active) or control VNS followed by home-based rehabilitation through day 90 (blinded phase). The control VNS group then crossed over to receive 6 weeks of in-clinic Active VNS. Participants in both groups then continued a long-term home exercise program with self-administered Active VNS. Main Outcome MeasuresFugl-Meyer Assessment for Upper Extremity (FMA-UE) and Wolf Motor Function Test (WMFT) Functional scores were evaluated at the end of in-clinic therapy and day 90. Since both groups were subsequently receiving home-based rehabilitation with Active VNS during the long term, follow-up outcome assessments were pooled for the analyses at 6, 9, and 12 months, as previously reported. Here, we report pooled analysis of outcomes beyond 1 year. ResultsOne year after Paired VNS therapy, FMA-UE improved by an average of 9.2±8.2 points, as previously reported. Overall, the 2- and 3-year FMA-UE gain from baseline was 11.4±8.7 (P<.001) and 14.8±10.2 points (P<.001), respectively. At years 2 and 3, FMA-UE improved by an additional 2.9 (P=.03 for change vs year 1, n=14) and 4.7 (P=.02 for change vs year 1, n=14) points, respectively. At year 1, 73% (11/15) of participants were responders (FMA-UE change ≥6) and by year 3, 85.7% (12/14) were responders. At years 2 and 3, the WMFT score improved by an additional 0.21 points (P=.03 for change vs year 1, n=15) and 0.42 points (P=.01 for change vs year 1, n=13), respectively. Responder rate (WMFT change ≥0.4) was 46.6% (7/15), 73.3% (11/15), and 69.2% (9/13) at years 1, 2, and 3, respectively. Long-term significant improvements were also observed for Motor Activity Log (MAL) and Stroke Impact Scale, Hand section (SIS-Hand). There were no serious long-term adverse events from the stimulation. ConclusionsSignificant effects of Paired VNS therapy at 1 year were maintained at years 2 and 3, and further improvements in both impairment and function were observed in years 2 and 3. These changes were associated with improvements in measures of activity and participation.

Effect of post-harvest processing methods on the microbial safety of edible seaweed

The American seaweed industry is growing, primarily into the edible sector, and more seaweed products are available for human consumption. It is necessary to evaluate the safety of industry’s current post-harvest storage and processing methods to ensure the risk of foodborne pathogens on edible seaweed remains low. We evaluated the pathogen load of edible kelp post-harvest under three different storage temperatures (4˚C, 10˚C, 20˚C) and two different drying methods (air- and freeze-drying). The focal pathogens for this research included: Listeria monocytogenes, Salmonella enterica, Staphylococcus aureus, pathogenic Escherichia coli, Vibrio vulnificus and Vibrio parahaemolyticus. We tested all six pathogens under each treatment condition on both sugar kelp (Saccharina latissima) and rockweed (Ascophyllum nodosum) as these are the most commonly farmed and wild-harvested species in Maine, respectively. We inoculated a known concentration of pathogen onto freshly harvested kelp, treated it under a storage temperature or drying method, and sampled it over time to determine the impact of treatment on pathogen load. Our results showed that storage at 20˚C can lead to replication while storage at 4˚C and 10˚C halted the replication of focal pathogens. Both air-drying and freeze-drying produced significant log scale reductions in surface pathogen load for all focal pathogens. Additionally, air-drying reduced pathogen load more than freeze-drying for a majority of pathogens and storing dried kelp for 6-weeks further reduced pathogen load across all cases. These results are promising for industry as they corroborate historical evidence that current post-harvest storage and processing conditions are producing products safe for human consumption.

Transient and periodic steady-state characteristics of the local heat transfer measurement by thermal perturbation with Gaussian power density distribution

The local heat transfer coefficient measurement with temperature oscillation induced by periodic thermal perturbation – usually via a Gaussian laser beam, was investigated for the impact of the spikiness (i.e., the standard deviation) elaborated in comparison with the analytical model for dimensional analysis. The statistically more robust technique that relies on the linearity of the spatial phase distribution of the test point array was favored when the target Biot number approaches unity in terms of its order of magnitude. The preferred upper limit for thermographic scanning was discussed as the simplification of later data processing is concerned. Nonetheless, the time elapsed for an acceptable periodic steady state, which in principle leans to the higher end of the target Biot number spectrum in a log scale, indicates the benefit from the time series of pointwise temperature measurement – as in the conventional single-blow testing, where the effect of spikiness, as well as that of the location of individual test point, holds. Note that the vicinity as the target Biot number approaches unity was again observed with higher preference.

Architecture of intraplate strike-slip fault zones in the Yanchang Formation, Southern Ordos Basin, China: Characterization and implications for their control on hydrocarbon enrichment

Commercial discoveries in the Ordos, Tarim, and Sichuan Basins of China have aroused widespread interest in strike-slip fault-controlled reservoirs. The productivity of different wells, however, can vary within one strike-slip fault zone, suggesting that variability in fault zone architecture controls hydrocarbon enrichment. To date, very few studies have finely and quantitatively explored fault zone architecture in the southern Ordos Basin, inhibiting hydrocarbon development. With the goal of understanding the architecture variability and scale of strike-slip fault zones in the subsurface, we carried out a refined and quantitative study of faults in the Jinghe Oilfield in the southern Ordos Basin by integrating outcrops, wellbore cores, well logs, and 3D seismic data. We quantitatively constrained the subsurface damage zone boundaries according to the slope changes in the cumulative CFI (comprehensive fracture index log) curves at logging scale and the cumulative FSI (fault shape index seismic attribute) curves at seismic scale. We proposed a model highlighting the effects of fault segmentation, architectural configuration, and damage zone asymmetry on the variability of fault zone architecture. Results showed that strike-slip faults can be divided into transtensional, pure strike-slip, and transpressional segments along the fault strike, with transtensional and pure strike-slip segments dominant in the Jinghe Oilfield. These segments exhibited six types of geometric structures, forming complex architectures with multi-fault cores and multi-damage zones surrounding the main and secondary faults. Each segment was further complicated by three configurations of gouge, breccia, and damage zones along the fault dip. The damage zone asymmetry further increased the architecture variability, with the fracture density and damage zone width of the hanging wall being greater than those of the footwall. Quantitative analysis showed that the fault zone width was the greatest for transtensional segments, intermediate for transpressional segments, and the lowest for pure strike-slip segments. And there was a positive linear correlation between the fault core width and the fault zone width (including the fault core and damage zone). Fault segmentation and damage zone asymmetry affected the hydrocarbon enrichment along the fault strike and dip within one strike-slip fault zone. We conclude that damage zones in transtensional segments, particularly in hanging walls, are primary targets for hydrocarbon development in the southern Ordos Basin.

Absence of logarithmic and algebraic scaling entanglement phases due to the skin effect

Measurement-induced phase transition in the presence of competition between projective measurement and random unitary evolution has attracted increasing attention due to the rich phenomenology of entanglement structures. However, in open quantum systems with free fermions, a generalized measurement with conditional feedback can induce skin effect and render the system short-range entangled without any entanglement transition, meaning the system always remains in the ``area law'' entanglement phase. In this work, we demonstrate that the power-law long-range hopping does not alter the absence of entanglement transition brought on by the measurement-induced skin effect for systems with open boundary conditions. In addition, for the finite-size systems, we discover an algebraic scaling $S(L, L/4)\sim L^{3/2-p}$ when the power-law exponent $p$ of long-range hopping is relatively small. For systems with periodic boundary conditions, we find that the measurement-induced skin effect disappears and observe entanglement phase transitions among ``algebraic law'', ``logarithmic law'', and ``area law'' phases.

Using a Synthetic Borehole Model to Determine the Pore Aspect Ratio Dependence of Velocities from Acoustic Well-Logging Data

Revealing the elastic wave properties of carbonate rocks with complex pore structures and improving the reliability of carbonate reservoir descriptions have always been a global challenge in the field of carbonate geophysical exploration. In this study, we established a synthetic borehole model by selecting different particle sizes of cement, carbonate cuttings, and micro-silicon as the matrix, and silicon disks as the pores in carbonate rocks. We conducted four sets of low-porosity (0-3%) borehole models with different pore aspect ratios (ARs) and measured the P- and S-wave velocities ( V P and V S ) at the well-logging scale obtained from an acoustic logging system with one source and two receivers. The results indicate that the relationship between velocities and porosities in these borehole models follows a linear relation, with the pore AR significantly influencing the velocities at any given porosity. The velocity variation caused by pore AR reaches 560 m/s and 410 m/s at 3% porosity for the P-wave and S-wave within the AR range of 0.017-0.13. The theoretical DEM models provide a high and broad estimation of V P and V S at the well-logging scale in our measurement. They could perform better in fractured formation than in dissolved porous formation in carbonate reservoirs. The linear relation of V P and V S is independent of the pore AR and is effective for both fractured and dissolved porous formations. The change of V P / V S in different pore AR is more responsive to porosity and nonlinear dependent on the pore AR. The relationship between the defined normalized V P and V S indicates the pore AR has a more significant effect on V S than V P in our model. The constructed borehole models provide a unique opportunity for evaluating the availability of rock physics models at an acoustic logging scale. The study’s findings have significant implications for improving the reliability of carbonate reservoir descriptions and enhancing the accuracy of geophysical exploration in carbonate rocks with complex pore structures.

Variational Quantum Algorithms for Computational Fluid Dynamics

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required hardware but also in identifying the most promising application areas and developing the corresponding quantum algorithms. The availability of intermediate-scale noisy quantum computers is now propelling the developments of novel algorithms, with applications across a variety of domains, including in aeroscience. Variational quantum algorithms are particularly promising because they are comparatively noise tolerant and aim to achieve a quantum advantage with only a few hundred qubits. Furthermore, they are applicable to a wide range of optimization problems arising throughout the natural sciences and industry. To demonstrate the possibilities for the aeroscience community, we give a perspective on how variational quantum algorithms can be used in computational fluid dynamics. We discuss how classical problems are translated into quantum algorithms and their logarithmic scaling with problem size. For an explicit example, we apply this method to Burgers’s equation in one spatial dimension. We argue that a quantum advantage over classical computing methods could be achieved by the end of this decade if quantum hardware progresses as currently envisaged and emphasize the importance of joining up development of quantum algorithms with application-specific expertise to achieve a real-world impact.

The Growth Curve of Microbial Cultures: A Model for a Visionary Reappraisal

A phenomenological model of planktonic microbial cultures, reported in previous papers, suggests that the whole growth progress seems planned by the microbial population since a pre-growth latency phase, during which the population level remains at its starting level. This model is in line with recent suggestions about the behavior of complex systems, as long as it allows for the gathering of the growth trends of a number of real batch cultures in a single master plot of reduced variables, in spite of their metabolic and physiological differences. One important issue of the model concerns the origin of the time scale for the microbes that can differ from that for the observer. The present paper reports some consequences of the model in view of its potential use in predictive microbiology and proposes an extension to the steady and decay phases of the culture evolution suggesting that, consistent with the assumptions about the growth phase, the decay occurs by a scan of the cell generation steps. This view leads to the conclusion that the steady phase between growth and decay trends actually corresponds to the loss of the oldest cell generations, which represents minor fractions of the microbial population. Such early decay is almost undetectable in a log scale, looking like a steady phase. To account for cases that show a broad maximum instead of an intermediate steady trend, a single continuous function, still related to the model, can describe the whole growth and decay trend of the microbial culture.

Varying Calcium Abundances in Solar Flares Seen by the Solar Maximum Mission

We report on calcium abundance A(Ca) estimates during the decay phases of 194 solar X-ray flares using archived data from the Bent Crystal Spectrometer (BCS) on the Solar Maximum Mission (operational 1980–1989). The abundances are derived from the ratio of the total calcium X-ray line emission in BCS channel 1 to that in neighboring continuum, with temperature from a satellite-to-resonance line ratio. Generally, the calcium abundance is found to be about 3 times the photospheric abundance, as previously found, indicating a “first ionization potential” (FIP) effect for calcium, which has a relatively low FIP value. The precision of the abundance estimates (referred to hydrogen on a logarithmic scale with A(H) = 12), is typically ∼± 0.01, enabling any time variations of A(Ca) during the flare decay to be examined. For a total of 270 short time segments with A(Ca) determined to better than 2.3% accuracy, many (106; 39%) showed variations in A(Ca) at the 3σ level. For the majority, in 74 (70%) of these 106 segments A(Ca) decreased with time, and for 32 (30%) A(Ca) increased with time. For 79 out of 270 (29%) we observed constant or nearly constant A(Ca), and the remaining 85 (31%) with irregular time behavior. A common feature was the presence of discontinuities in the time behavior of A(Ca). Relating these results to the ponderomotive force theory of Laming, we attribute the nature of varying A(Ca) to the emergence of loop structures in addition to the initial main loop, each with its characteristic calcium abundance.

A real-time underwater soundscape classification system

The study of underwater soundscapes, pioneered by Dr. Jeff Nystuen, includes information about geophonic, biological, and anthropogenic processes, many of which have distinct spectral characteristics. The contributors to the underwater ambient sound field can be quantified and classified using knowledge of these spectra. Long-term acoustic data recordings from a wide variety of depths and locations with high sampling frequencies have been analyzed to develop a robust soundscape classification algorithm based on Dr. Nystuen’s methods. Each one-minute of data has been evaluated to classify the soundscape into wind, rainfall, drizzle, heavy shipping, light shipping, other vessel activity, and biological phenomena. The power spectral density (PSD) level at twelve frequencies in the range of 0.03–30 kHz, as well as the spectral slope for the frequency range between 8 and 15kHz and kurtosis are used for the passive classification algorithm. After classification, the wind speed was quantified as a cubic function of PSD at 6 kHz and recording depth. The wind speed estimated from the acoustics compared very well to satellite data for speeds lower than 15 m/s. The classification algorithms are being embedded on a processor using Xilinx’s Zynq System-on-Chip that produces a 32-kHz hybrid millidecade spectrum in real-time on a logarithmic scale.

Understanding 'it depends' in ecology: a guide to hypothesising, visualising and interpreting statistical interactions.

Ecologists routinely use statistical models to detect and explain interactions among ecological drivers, with a goal to evaluate whether an effect of interest changes in sign or magnitude in different contexts. Two fundamental properties of interactions are often overlooked during the process of hypothesising, visualising and interpreting interactions between drivers: the measurement scale - whether a response is analysed on an additive or multiplicative scale, such as a ratio or logarithmic scale; and the symmetry - whether dependencies are considered in both directions. Overlooking these properties can lead to one or more of three inferential errors: misinterpretation of (i) the detection and magnitude (Type-D error),and (ii) the sign of effect modification (Type-S error); and (iii) misidentification of the underlying processes (Type-A error). We illustrate each of these errors with a broad range of ecological questions applied to empirical and simulated data sets. We demonstrate how meta-analysis, a widely used approach that seeks explicitly to characterise context dependence, is especially prone to all three errors. Based on these insights, we propose guidelines to improve hypothesis generation, testing, visualisation and interpretation of interactions in ecology.

How to Choose a Magnitude Interval to Evaluate the Slope of the Magnitude-frequency Graph

In modern seismological practice, to describe the distribution of magnitudes, the Gutenberg-Richter law is widely used, one of the parameters of which is the b-value (the slope of the magnitude-frequency graph on a log scale). Authors propose new approaches to the problem of adequate and efficient statistical estimation of this parameter. The problem of the correct choice of the magnitude interval is discussed, on which the straightness of the Gutenberg-Richter law is observed with an acceptable degree of accuracy and which should be used to estimate the b-value. An efficient method of accounting for discreteness and aggregation of magnitudes in earthquake catalogs (the maximum likelihood method for discrete distributions) is proposed. The problem of changes in time of the lower limit of representative earthquakes registration is considered and a statistical approach is proposed for their description.

Double Superposed Epoch Analysis of Geomagnetic Storms and Corresponding Solar Wind and IMF in Solar Cycles 23 and 24

AbstractThe weakest solar cycle 24 (SC24, 2010–2019) in 100 years was 1/3rd less active compared to the previous solar cycle 23 (SC23, 1996–2009). We identify 135 and 61 ICME (interplanetary coronal mass ejection) driven clear geomagnetic storms (DstMin ≤ −50 nT) in SC23 and SC24, respectively, giving a reduction of 55% storms in SC24, and present the double superposed epoch analysis (DSEA) of the storms/activities in SC23 and SC24 using the Dst, symmetric H (SymH), Kp and AE indices. The DSEA method for the corresponding solar wind velocity V, north‐south component of the interplanetary magnetic field (IMF Bz) and the product VBz are also presented. Compared to SC23, the maximum storm/activity intensity in SC24 reduces by 52%, 12%, and 45% at low, mid and high latitudes and the corresponding maxima in ‐VBz, V, and ‐Bz reduce by 39%, 17%, and 38%, respectively. The epoch average storm/activity intensity reduces by 27%, 11%, and 4% at low, mid and high latitudes and average maxima in ‐VBz, V, and ‐Bz reduce by 24%, 14%, and 13%, respectively. The results seem to reveal that the average reduction in the main driver ‐VBz (∼24%) might have caused nearly the same and equal average storm/activity intensity reductions in all latitudes (∼25%), though the irregular nature of the AE index makes the reduction very small (4%) at high latitudes, and small (∼11%) at mid latitudes mainly due to the small (0–9) quasi logarithmic scale of the Kp index.

A Quantum Algorithm for the Sub-graph Isomorphism Problem

We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number of qubits that scales logarithmically with the number of vertices of the graphs; and (2) on a new ansatz that can efficiently probe the permutation space. Simulations are then presented to showcase the approach on graphs up to 16 vertices, whereas, given the logarithmic scaling, the approach could be applied to realistic sub-graph isomorphism problem instances in the medium term.

Efficacy of antiseptics and chemomechanical methods for dentin caries lesions: A systematic review with GRADE approach.

Selective caries removal aims to remove carious tissue in deep dentin lesions. However, a discussion stands on the value of antiseptics and chemomechanical adjuvant methods to reduce the bacterial load on residual caries lesions. This systematic review has addressed two main clinical questions to compare the antimicrobial efficacy of available methods using (1) antiseptic or (2) chemomechanical agents before restoring dentin carious lesions. We included randomized and non-randomized controlled trials (RCTs/ NRCTs). We searched eight databases from inception to October 2021. Paired reviewers independently screened studies, extracted data, and assessed the risk of bias. The primary outcome was the reduction in the number of total bacterial in dentin, whereas secondary outcomes were reduction in the number of Lactobacillus and Streptococcus. We used the ratio of ratio of post-treatment to baseline means between two interventions in the logarithmic scale as a proper effect measure. Certainty of evidence was assessed with the Grading of Recommendations, Assessment, Development and Evaluation approach. We included 14 RCTs and 9 NRCTs, with nine interventions. Regardless the method, the number of bacteria at baseline was similar or exceeded that after the intervention, particularly in NRCTs. The evidence was inconclusive for most comparisons. Among antiseptic agents, chlorhexidine (CHX) resulted in an average of 1.14 times [95% confidence interval (CI): 1.08-1.21] more total bacterial than photodynamic therapy in RCTs. Among NRCTS, the natural agents resulted in five times more total bacterial than CHX (95% CI: 2-11). For chemomechanical methods, the control resulted in eight times (95% CI: 4-17) more total bacterial than Carisolv (SHAA). The certainty of the evidence was very low for all comparisons showing uncertainty whether one treatment could be more effective than another for dentin disinfection. So far, exclusively removing soft carious dentin would be enough to reduce the bacterial count.

Serum 25-Hydroxyvitamin D Levels and Youth-Onset Type 2 Diabetes: A Two-Sample Mendelian Randomization Study.

Observational studies have linked vitamin D insufficiency to pediatric type 2 diabetes (T2D), but evidence from vitamin D supplementation trials is sparse. Given the rising prevalence of pediatric T2D in all ethnicities, determining the protective role of vitamin D has significant public health importance. We tested whether serum 25-hydroxyvitamin D (25OHD) levels are causally linked to youth-onset T2D risk using Mendelian randomization (MR). We selected 54 single-nucleotide polymorphisms (SNPs) associated with 25OHD in a European genome-wide association study (GWAS) on 443,734 individuals and obtained their effects on pediatric T2D from the multi-ethnic PRODIGY GWAS (3006 cases/6061 controls). We applied inverse variance weighted (IVW) MR and a series of MR methods to control for pleiotropy. We undertook sensitivity analyses in ethnic sub-cohorts of PRODIGY, using SNPs in core vitamin D genes or ancestry-informed 25OHD SNPs. Multivariable MR accounted for the mediating effects of body mass index. We found that a standard deviation increase in 25OHD in the logarithmic scale did not affect youth-onset T2D risk (IVW MR odds ratio (OR) = 1.04, 95% CI = 0.96-1.13, p = 0.35) in the multi-ethnic analysis, and sensitivity, ancestry-specific and multivariable MR analyses showed consistent results. Our study had limited power to detect small/moderate effects of 25OHD (OR of pediatric T2D < 1.39 to 2.1). In conclusion, 25OHD levels are unlikely to have significant effects on the risk of youth-onset T2D across different ethnicities.

Soil Moisture Change Detection with Sentinel-1 SAR Image for Slow Onsetting Disasters: An Investigative Study Using Index Based Method

Understanding physical processes in nature, including the occurrence of slow-onset natural disasters such as droughts and landslides, requires knowledge of the change in soil moisture between two points in time. The study was conducted on a relatively bare soil, and the change in soil moisture was examined with an index called Normalized radar Backscatter soil Moisture Index (NBMI) using Sentinel-1 satellite data. Along with soil moisture measured with a probe on the ground, a study of correlation with satellite imagery was conducted using a Multiple Linear Regression (MLR) model. Furthermore, the Dubois model was used to predict soil moisture. Results have shown that NBMI on a logarithmic scale provides a good representation of soil moisture change with R2~86%. The MLR model showed a positive correlation of soil moisture with the co-polarized backscatter coefficient, but an opposite correlation with the surface roughness and angle of incidence. The results of the Dubois model showed poor correlation of 44.37% and higher RMSE error of 17.1, demonstrating the need for detailed and accurate measurement of surface roughness as a prerequisite for simulating the model. Of the three approaches, index-based measurement has been shown to be the most rapid for understanding soil moisture change and has the potential to be used for understanding some mechanisms of natural disasters under similar soil conditions.

Large deviations for subcomplex counts and Betti numbers in multiparameter simplicial complexes

We consider the multiparameter random simplicial complex as a higher dimensional extension of the classical Erdős–Rényi graph. We investigate appearance of “unusual” topological structures in the complex from the point of view of large deviations. We first study upper tail large deviation probabilities for subcomplex counts, deriving the order of magnitude of such probabilities at the logarithmic scale precision. The obtained results are then applied to analyze large deviations for the number of simplices of the multiparameter simplicial complexes. Finally, these results are also used to deduce large deviation estimates for Betti numbers of the complex in the critical dimension.