Rice Formula Research Articles

Formulation and Characterization of Analog Rice Using Arrowroot (Maranta arundinacea L.) and Hibiscus Flower (Hibiscus rosa sinensis L.)

Background: Efforts to reduce high-carbohydrate consumption from rice include the development of analog rice from alternative sources such as arrowroot tubers (Maranta arundinacea L.). Proper formulation is crucial for producing analog rice with optimal quality, taste, and characteristics resembling conventional rice, while maintaining functional properties to meet carbohydrate and nutritional needs. Hibiscus (Hibiscus rosa-sinensis L.), which is rich in flavonoids, saponins, and anthocyanins, can enhance these formulations. Objective: The objective of this study was to evaluate the composition of a blend of arrowroot tubers (M. arundinacea L.) and hibiscus (H. rosa-sinensis L.) as a rice substitute. Methods: This study used 50 untrained panelists to conduct organoleptic tests on the shape, color, aroma, taste, and texture of rice and analog rice using five formulas (F1, F2, F3, F4, and F5). Furthermore, physical characteristics were tested, including the color index, 1000-grain weight, bulk density, and starch digestibility. Results: The characteristics test proved that all analog rice formulas had an average hedonic score in the range of 3.73-3.90; lower bulk Density than rice with a bulk density of 0.83 ± 0.02 g/mL; starch digestibility in the range of 0.62-0.67 g/mL; and has a yellow-red color range. Conclusion: The best and most preferred rice analog is Formula 5 (F5), with a composition of arrowroot tubers 57.8%, hibiscus 5.1%, mocaf 12.6%, GMS 0.6%, and water 23.9%.

DEVELOPMENT OF ANALOG RICE FROM PURPLE CORN AND SEAWEED Gracillaria sp POTENTIAL AS HIGH-FIBER FUNCTIONAL FOOD

Analog rice (imitation rice) is made from ingredients such as cereals and tubers whose shape and nutritional composition are similar to rice. The main ingredients that can be used to create analog rice are purple corn and seaweed which have good nutritional value. The purpose of this study was to determine the formulation of analog rice with high fiber. This study has 4 treatments, namely K1 (polished rice), K2 (seaweed 5%), K3 (seaweed 10%), and K4 (seaweed 15%). The highest dietary fiber is 5.77%, low air content is 7.09%, has an ash content ranging from 0.75 - 6.5%, fat content ranges from 1.24 - 5.66%, Carbohydrates range from 71.29 - 77, 48%., protein 7.09 - 8.35%. Color analysis of analog rice parameter L * (brightness) ranges from 38.20 - 40.66. WI value ranges from 59.43 to 60.68, a* (red) value ranges from 5.97 to 5.39, b* (yellow) value ranges from 9.8 to 10.73, and tranparancy value ranges from 59.43 to 60.68. The results of the organoleptic test of all parameters show that the highest organoleptic value is obtained in milled rice and in the analog rice formula which has the highest value, namely K2 (5% seaweed). Keywords: Analog Rice, Purple Corn, Seaweed, Dietary Fiber

Probabilistic risk analysis of local verification of Load Model 1 in Eurocode for Soil-Steel Composite bridges in Sweden

Bridges must be designed to ensure safety for all users. At the same time, the design should be performed with an appropriate risk level. In Sweden, Soil-Steel Composite bridges (SSCB) are the most common bridge type. For SSCB, local verification of Load Model 1 in Eurocode is most often governing the design. The objective of this study was to investigate whether local verification of LM1 load case could be modified without decreasing the agreed risk level in Eurocode. Weight in motion measurements from real traffic were extrapolated with Rice formula. Monte Carlo simulations were used to simulate the 1000-year return period event to obtain the acceptable risk level as prescribed in Eurocode. The results show that the local verification of LM1 is conservative, considering the acceptable risk level in Eurocode. With a modified implementation of local verification, this paper shows that a potential saving of up to 14% in terms of economic cost and CO2-equivalents is possible. A modified implementation of local verification of LM1 in Eurocode for SSCB is proposed, which could reduce the climate impact by up to 14% associated to the construction of new SSCB in Sweden.

Association Rules Analysis for Continuous Chicken Egg Traits Dataset

This study aims to apply the Apriori association rule algorithm on 14 continuous egg quality traits recorded from 4320 eggs of three commercial white-laying chicken lines. In the study all the continuous data were discretized using Equal-Width-Interval method based the number of intervals obtained with Rice formula. Association rules analysis on the discretized dataset resulted with a total of 349 rules consists of 3 and 4 items. According to the top five rules by support and confidence, some important associations were obtained between the certain value ranges of the traits egg weight, egg width, egg length, shell thickness, and shell breaking strength when compared to the others. The appropriate biological and economic interpretations of the obtained rules may contribute to the poultry industry in practice.

Regional differences in diagnosis and management of cow's milk allergy.

Various guidelines for the diagnosis and management of cow's milk allergy (CMA) have been published. This study aimed to compare voting outcomes of experts from Mexico, the Middle East, and the European Society of Pediatric Gastroenterology Hepatology and Nutrition (ESPGHAN) on statements regarding CMA. The 3 expert groups voted on the same 10 statements. Each participant voted anonymously using a score of 0-9 (≥6 meant agreement; <5 reflected disagreement). If <75% of the participants agreed with the statement, it was rejected. None of the groups was aware of the voting outcomes of another group. There was broad consensus amongst the 3 groups. Agreement was reached that infant colic as a single manifestation is not suggestive of CMA. All groups confirmed that an extensively hydrolysed formula is the preferred elimination diet in mild/moderate CMA cases; however, hydrolysed rice formula is an alternative. Amino acid-based formulas should be reserved for infants with severe symptoms. The discrepancy in voting outcomes regarding soy formulas highlights the differences in opinions. Two of 13 ESPGHAN experts (15%), 1 of 14 Middle East experts (7%), and 6 of 26 Mexican experts (23%) disagreed with the statement that soy formula should not be the first choice for the diagnostic elimination diet but can be considered in some cases for economic, cultural, and palatability reasons. All of the ESPGHAN and Mexican experts agreed that there was no added value of probiotics, prebiotics, or synbiotics to the efficacy of elimination diets on CMA, whereas 3 of 14 Middle East experts (21%) determined that there was sufficient evidence. Although all statements were accepted by the 3 groups, there were relevant differences illustrating variations according to geography, culture, cost, and formula availability. These findings emphasize the need for region-specific guidelines.

Semi-analytical solutions of kinked edge cracks

A surface crack may advance either by further penetrating inward or by kinking out in response to possible variations in driving force or material properties. This paper provides a general approach to solve the planar elastic boundary value problem (BVP) of a kinked edge crack in a half-space. Semi-analytical solutions to BVPs with far-field uniform tension and concentrated loads on the free surface are given. The solution enable us to derive related information for reliability analysis, including stress fields, stress intensity factors (SIFs), and crack opening displacement (COD). An extension to the Cotterell–Rice formula (Cotterell and Rice, 1980) on SIFs for infinitesimal kinks is supplied, which is applicable to cracks with kinked segments of arbitrary length. Zooming in on a broadly concerned BVP of a cross-coating crack in a coating–substrate with a kink in the interface, we show the SIFs of the kink tip following an empirical formula K∗=αexp(−βah)+K∞∗ as a/h>0.2, where a is the length of the interface segment and h the coating thickness, and K∞∗ is the asymptotic solution by Thouless et al. (1987, 1989). The formula is in accord with existing solutions on the two asymptotic limits of the kinked part.

A novel konjac rice formula with glucomannan and tapioca starch improve postprandial glycemic response – a randomized single-blind clinical trial

PurposeDue to white rice’s association with diabetes and other chronic diseases in many Asian countries, many industries are working to develop high-fiber rice substitutes with similar organoleptic characteristics. Konjac rice (KR) is a promising option, but maintaining its optimal fiber content for health benefits while preserving its ideal sensory profile remains a challenge. This study aims to investigate whether a KR formula, combining tapioca flour and glucomannan gel, possesses similar organoleptic attributes to white rice while preventing glycemic response elevation.Design/methodology/approachIn a six-week randomized single-blind clinical trial, 13 normoweight nondiabetic subjects received varying konjac-based rice and white rice ratios. Blood glucose levels were measured at intervals, and glycemic response was assessed using incremental area under the curve (iAUC). Visual analog scale gauged satiety, and organoleptic properties were evaluated.FindingsSubstituting white rice with pure and partial konjac-based rice significantly lowered postprandial blood sugar levels and glycemic response (p = 0.002). iAUC for pure KR and KR 1:1 was notably lower than white rice (p = 0.002). Subjects reported a sense of fullness comparable to white rice, with no significant organoleptic score differences (p = 0.260).Research limitations/implicationsThe study’s generalizability is compromised due to the limited number of participants, impacting external validity. The examined parameters offer a rough understanding of konjac grain’s impact on postprandial glycemic responses but do not elucidate underlying mechanisms or the duration of its inhibitory effect on glucose absorption. Long-term effects on metabolic, hormonal parameters and the colon’s microbial flora composition and function remain unexplored, constraining comprehensive insights into konjac grain’s extended implications.Practical implicationsThis study introduces a novel KR formula to address the escalating diabetes risks associated with white rice consumption. Substituting white rice with KR significantly reduces postprandial blood sugar levels, highlighting its potential in preventing type 2 diabetes (T2D). Tapioca flour enhances palatability, making KR a viable option. While promising, long-term effectiveness and safety require further research, emphasizing comprehensive lifestyle interventions. The study contributes valuable insights to innovative dietary strategies for prevalent health conditions, emphasizing the need for ongoing efforts in public health.Social implicationsWhite rice, a staple in Asian societies, is linked to a heightened risk of T2D due to increased production and inadequate dietary fiber. This connection contributes to the economic burden on governments through health insurance and lost productivity. Encouraging alternatives rich in fiber can mitigate this burden, offering a socioeconomically beneficial solution to preventable chronic diseases.Originality/valueThis trial demonstrates konjac-based rice’s potential in curbing glycemic responses, hinting at its role in preventing T2D. Glucomannan’s viscosity, satiety induction and potential gut health impact are highlighted. Further research is warranted for long-term effectiveness and safety. These findings contribute to the growing evidence supporting glucomannan as a valuable tool in addressing prevalent health conditions.

Symptoms and management of cow's milk allergy: perception and evidence.

The diagnosis and management of cow's milk allergy (CMA) is a topic of debate and controversy. Our aim was to compare the opinions of expert groups from the Middle East (n = 14) and the European Society of Paediatric Gastroenterology, Hepatology and Nutrition (ESPGHAN) (n = 13). These Expert groups voted on statements that were developed by the ESPGHAN group and published in a recent position paper. The voting outcome was compared. Overall, there was consensus amongst both groups of experts. Experts agreed that symptoms of crying, irritability and colic, as single manifestation, are not suggestive of CMA. They agreed that amino-acid based formula (AAF) should be reserved for severe cases (e.g., malnutrition and anaphylaxis) and that there is insufficient evidence to recommend a step-down approach. There was no unanimous consensus on the statement that a cow's milk based extensively hydrolysed formula (eHF) should be the first choice as a diagnostic elimination diet in mild/moderate cases. Although the statements regarding the role for hydrolysed rice formula as a diagnostic and therapeutic elimination diet were accepted, 3/27 disagreed. The votes regarding soy formula highlight the differences in opinion in the role of soy protein in CMA dietary treatment. Generally, soy-based formula is seldom available in the Middle-East region. All ESPGHAN experts agreed that there is insufficient evidence that the addition of probiotics, prebiotics and synbiotics increase the efficacy of elimination diets regarding CMA symptoms (despite other benefits such as decrease of infections and antibiotic intake), whereas 3/14 of the Middle East group thought there was sufficient evidence. Differences in voting are related to geographical, cultural and other conditions, such as cost and availability. This emphasizes the need to develop region-specific guidelines considering social and cultural conditions, and to perform further research in this area.

Lead Levels in the Most Consumed Mexican Foods: First Monitoring Effort.

Globally, there is growing concern over the presence of lead (Pb) in foods because it is a heavy metal with several toxic effects on human health. However, monitoring studies have not been conducted in Mexico. In this study, we estimated the concentrations of Pb in the most consumed foods and identified those that exceeded the maximum limits (MLs) for Pb in foods established by the International Standards. Based on the Mexican National Health and Nutrition Survey, 103 foods and beverages were selected and purchased in Mexico City retail stores and markets. Samples were analyzed twice using atomic absorption spectrophotometry. Values above the limit of quantification (0.0025 mg/kg) were considered to be detected. The percentage of detected values was 18%. The highest concentration was found in infant rice cereal (1.005 mg/kg), whole wheat bread (0.447 mg/kg), pre-cooked rice (0.276 mg/kg), black pepper (0.239 mg/kg), and turmeric (0.176 mg/kg). Among the foods with detected Pb, the levels in infant rice cereal, whole wheat bread, pre-cooked rice, and soy infant formula exceeded the MLs. The food groups with the highest percentages of exceeded MLs were baby foods (18%) and cereals (11%). Monitoring the concentration of contaminants in foods is essential for implementing food safety policies and protecting consumer health.

World Allergy Organization (WAO) Diagnosis and Rationale for Action against Cow's Milk Allergy (DRACMA) guideline update – XII – Recommendations on milk formula supplements with and without probiotics for infants and toddlers with CMA

BackgroundCow's milk allergy (CMA) is the most common food allergy in infants. The replacement with specialized formulas is an established clinical approach to ensure adequate growth and minimize the risk of severe allergic reactions when breastfeeding is not possible. Still, given the availability of multiple options, such as extensively hydrolyzed cow's milk protein formula (eHF-CM), amino acid formula (AAF), hydrolyzed rice formula (HRF) and soy formulas (SF), there is some uncertainty as to the most suitable choice with respect to health outcomes. Furthermore, the addition of probiotics to a formula has been proposed as a potential approach to maximize benefit. ObjectiveThese evidence-based guidelines from the World Allergy Organization (WAO) intend to support patients, clinicians, and others in decisions about the use of milk specialized formulas, with and without probiotics, for individuals with CMA. MethodsWAO formed a multidisciplinary guideline panel balanced to include the views of all stakeholders and to minimize potential biases from competing interests. The McMaster University GRADE Centre supported the guideline-development process, including updating or performing systematic evidence reviews. The panel prioritized clinical questions and outcomes according to their importance for clinicians and patients. The Grading of Recommendations Assessment, Development and Evaluation (GRADE) approach was used, including GRADE Evidence-to-Decision frameworks, which were subject to review by stakeholders. ResultsAfter reviewing the summarized evidence and thoroughly discussing the different management options, the WAO guideline panel suggests: a) using an extensively hydrolyzed (cow's milk) formula or a hydrolyzed rice formula as the first option for managing infants with immunoglobulin E (IgE) and non-IgE-mediated CMA who are not being breastfed. An amino-acid formula or a soy formula could be regarded as second and third options respectively; b) using either a formula without a probiotic or a casein-based extensively hydrolyzed formula containing Lacticaseibacillus rhamnosus GG (LGG) for infants with either IgE or non-IgE-mediated CMA.The issued recommendations are labeled as “conditional” following the GRADE approach due to the very low certainty about the health effects based on the available evidence. ConclusionsIf breastfeeding is not available, clinicians, patients, and their family members might want to discuss all the potential desirable and undesirable consequences of each formula in infants with CMA, integrating them with the patients' and caregivers’ values and preferences, local availability, and cost, before deciding on a treatment option. We also suggest what research is needed to determine with greater certainty which formulas are likely to be the most beneficial, cost-effective, and equitable.

On the empirical approximation to quantiles from Lugannani–Rice saddlepoint formula

Lugannani–Rice saddlepoint formula approximates the tail probability and the cumulative distribution function of the sample mean of independent and equally distributed variables. This note revisits Lugannani–Rice formula with a proposal for inverting it to approximate the quantile of the distribution empirically. The asymptotic behavior of the empirical approximation is assessed theoretically and its numerical accuracy for finite samples is studied and compared with the normal approximation and the second order Cornish-Fisher expansion by means of a simulation study. The outcomes of the simulation experiment shed light on the limitations of the empirical inversions of saddlepoint formulae to approximate quantiles.

Advanced separation of mineral oil aromatic hydrocarbons by number of aromatic rings using donor-acceptor-complex chromatography to extend on-line coupled liquid chromatography-gas chromatography

An automated implementation for a subfractionation of mineral oil aromatic hydrocarbons (MOAH) into a mono-/di-aromatic fraction (MDAF) and a tri-/poly-aromatic fraction (TPAF) is presented, which is highly demanded by the European Food Safety Authority (EFSA) respecting the genotoxic and carcinogenic potential of MOAH. For this, donor-acceptor-complex chromatography (DACC) was used as a selective stationary phase to extend the conventional instrumental setup for the analysis of mineral oil hydrocarbons via on-line coupled liquid chromatography-gas chromatography-flame ionization detection (LC-GC-FID). A set of six new internal standards was introduced for the verification of the MOAH fractionation and a quantification of MDAF and TPAF, respectively. The automated DACC approach was applied to representative petrochemical references as well as to food samples, such as rice and infant formula, generally showing well conformity with results obtained by state-of-the-art analysis using two-dimensional GC (GCxGC). Relative deviations of DACC/LC-GC-FID compared to GCxGC-FID methods regarding the ≥ 3 ring MOAH content ranged between -50 and +6 % (median: -2 %, all samples, only values above limit of quantification). However, crucial deviations mainly result from “border-crossing” substances, e.g., dibenzothiophenes or partially hydrogenated MOAH. These substances can cause overestimations of ≥ 3 ring MOAH fraction during GCxGC analysis due to co-elution, which is mostly avoided using the DACC approach. Furthermore, the DACC approach can help to minimize underestimations of toxicologically relevant ≥ 3 ring MOAH caused by an unavoidable loss of MOAH during epoxidation, since natural olefins, such as terpenes, predominantly elute in MDAF, which was exemplarily shown for an olive oil and a terpene reference. The presented approach can be implemented easily in existing LC-GC-FID setup for an automated and advanced screening of MOAH to lower the need for elaborate GCxGC analysis also in routine environments.

Characterization of Mixed Rice: Nutritional Value, Physicochemical Properties, Organoleptic, and Glycemic Index

The nutritional and physicochemical value of rice could be enhanced by mixing or combining white and brown rice with various beans. Besides nutritional and functional aspects, it is also crucial to consider organoleptic properties. Therefore, this study aimed to characterize nutritional value (proximate), physicochemical properties, organoleptic and Glycemic Index (GI) of mixed rice. A total of 10 mixed rice formulas, ranging from F1 to F10, and consisting of white rice, brown rice, black rice, aromatic rice, sticky rice, black-eyed peas and mung beans, were determined. These samples were analyzed for proximate, total phenolic compounds, pasting properties, and organoleptic tests (hedonic and ranking tests). Furthermore, 3 selected formulas based on the previous test were then evaluated for GI, and Glycemic Load (GL) was calculated. The results showed that adding black-eyed peas and mung beans (F9 and F10) increased the protein content of mixed rice while higher proportion of black or brown rice (F3 and F4) enhanced the fat content. The amylose content was decreased due to higher proportion of sticky rice (F6 and F8). Based on the hedonic test, the F1-F6 formula had a favorable rating. The ranking results indicated that F9 was better than F10, while F1 and F6 was the best among F1 to F4, as well as F5 to F8. Considering the constituent materials, F1, F6, F9 and commercial low GI rice were selected and tested for GI, and the test results showed 48.2, 54.7, 78.0, and 60.3, respectively. As a result, F1 and F6 have the potential to be developed as mixed rice because they have good nutritional value, physicochemical and organoleptic properties, as well as low GI.

Spanish Pediatricians' Positions Regarding Prevention, Diagnosis, Nutritional Management, and Challenges in Cow's Milk Protein Allergy.

Management of cow's milk protein allergy (CMPA) can vary depending on the experience and area of expertise of the clinician responsible for the patient's follow-up, which may or may not align with the recently published literature. To analyze the perspectives of Spanish pediatricians on this topic, a survey was conducted. The survey aimed to determine the current opinions and attitudes of 222 primary care and hospital pediatricians toward CMPA prevention and nutritional management. Participating pediatricians completed the questionnaire, providing insights into their daily clinical practices, including access to testing, attitudes with respect to various aspects of CMPA diagnosis, prevention, oral food challenges, and treatment. The findings revealed that pediatricians generally agree on the use of extensively hydrolyzed formulas (eHFs) to prevent CMPA in high-risk atopic children, despite limited evidence supporting the widespread use of this practice. However, consensus was lacking regarding the utility of formulas with prebiotics and probiotics for expediting tolerance development. In most cases, pediatricians preferred eHFs for the nutritional management of CMPA, followed by hydrolyzed rice formulas (HRFs), with amino-acid-based formulas (AAFs) being the third option. Certain issues remained controversial among pediatricians, such as prevention methods, symptom assessment, and the role of probiotics. These variations in management approaches reflect the influence of clinician experience and area of expertise, underscoring the need for standardized guidelines in this field.

Local convexity of the TAP free energy and AMP convergence for Z2-synchronization

We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength λ>1 (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly convex. Consequently, a natural-gradient/mirror-descent algorithm achieves linear convergence to this minimizer from a local initialization, which may be obtained by a constant number of iterations of Approximate Message Passing (AMP). This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy. We also analyze the finite-sample convergence of AMP, showing that AMP is asymptotically stable at the TAP minimizer for any λ>1, and is linearly convergent to this minimizer from a spectral initialization for sufficiently large λ. Such a guarantee is stronger than results obtainable by state evolution analyses, which only describe a fixed number of AMP iterations in the infinite-sample limit. Our proofs combine the Kac–Rice formula and Sudakov–Fernique Gaussian comparison inequality to analyze the complexity of critical points that satisfy strong convexity and stability conditions within their local neighborhoods.

Counting of level crossings for inertial random processes: Generalization of the Rice formula.

We address the counting of level crossings for inertial stochastic processes. We review Rice's approach to the problem and generalize the classical Rice formula to include all Gaussian processes in their most general form. We apply the results to some second-order (i.e., inertial) processes of physical interest, such as Brownian motion, random acceleration and noisy harmonic oscillators. For all models we obtain the exact crossing intensities and discuss their long- and short-time dependence. We illustrate these results with numerical simulations.

Accurate analytical calculation of the rate coefficient for the diffusion-controlled reactions due to hyperbolic diffusion.

Using an approach based on the diffusion analog of the Cattaneo-Vernotte differential model, we find the exact analytical solution to the corresponding time-dependent linear hyperbolic initial boundary value problem, describing irreversible diffusion-controlled reactions under Smoluchowski's boundary condition on a spherical sink. By means of this solution, we extend exact analytical calculations for the time-dependent classical Smoluchowski rate coefficient to the case that includes the so-called inertial effects, occurring in the host media with finite relaxation times. We also present a brief survey of Smoluchowski's theory and its various subsequent refinements, including works devoted to the description of the short-time behavior of Brownian particles. In this paper, we managed to show that a known Rice's formula, commonly recognized earlier as an exact reaction rate coefficient for the case of hyperbolic diffusion, turned out to be only its approximation being a uniform upper bound of the exact value. Here, the obtained formula seems to be of great significance for bridging a known gap between an analytically estimated rate coefficient on the one hand and molecular dynamics simulations together with experimentally observed results for the short times regime on the other hand. A particular emphasis has been placed on the rigorous mathematical treatment and important properties of the relevant initial boundary value problems in parabolic and hyperbolic diffusion theories.

Time-dependent structural reliability under nonstationary and non-Gaussian processes

With the increasing recognition of random and time-variant nature in structural responses, time-dependent reliability methods have become popular for structural reliability assessment in recent decades. This paper proposes a method that can determine the time-dependent reliability with accuracy and robustness under general stochastic processes, which are neither stationary nor Gaussian. It presents a detailed derivation of the first passage probability and upcrossing rate with a view to better understanding the time-dependent reliability theory. An idea is proposed to determine the upcrossing rate for any stochastic processes by combining the Rice formula with transformation of the stochastic processes. The proposed method is verified with both analytical solution and Monte Carlo simulation, and further tested with two practical examples. It is found in the paper that the proposed method is more accurate than the only existing analytical solution and yet more efficient than the Monte Carlo simulation with the same accuracy. It is also found that the proposed method is robust for any type of stochastic processes with a range of barrier levels and band widths. The significance of this proposed method is that it widens the application of time-dependent reliability methods to the assessment of practical structures during their service life.

Sharp complexity asymptotics and topological trivialization for the (p, k) spiked tensor model

Using precise random matrix theory tools and the Kac–Rice formula, we provide sharp O(1) asymptotics for the average number of deep minima of the (p, k) spiked tensor model. These sharp estimates allow us to prove that, when the signal-to-noise ratio is large enough, the expected number of deep minima is asymptotically finite as N tends to infinity and to establish the occurrence of topological trivialization by showing that this number vanishes when the strength of the signal-to-noise ratio diverges. We also derive an explicit formula for the value of the absolute minimum (the limiting ground state energy) on the N-dimensional sphere, similar to the recent work of Jagannath, Lopatto, and Miolane [Ann. Appl. Probab. 4, 1910–1933 (2020)].

Effective persistency evaluation via exact excursion distributions for random processes and fields

Finding the probability that a stochastic system stays in a certain region of its state space over a specified time—a long-standing problem both in computational physics and in applied and theoretical mathematics—is approached through the extended and multivariate Rice formula. In principle, it applies to any smooth process multivariate both in argument and in value given that efficient numerical implementations of the high-dimensional integration are available. The computational method offers an exact integral representation yielding remarkably accurate results and provides an alternative method of computing persistency probability and exponent for a physical system. It can be viewed as an implementation of path integration for a smooth Gaussian process with an arbitrary covariance. Its high accuracy is due to efficient computation of expectations with respect to high-dimensional nearly singular Gaussian distributions. For Gaussian processes, the computations are effective and more precise than those based on the Rice series expansions and the independent interval approximation. For the benchmark diffusion process, it produces the persistency exponent that is essentially the same as the recently obtained analytical value and surpasses accuracy, interpretability as well as control of the error, previous methods including the independent or Markovian approximation. The method solves the two-step excursion dependence for a stationary differentiable Gaussian process, in both theoretical and numerical sense. The solution is based on exact expressions for the probability density for one and two successive excursion lengths. The numerical routine RIND computes the densities using recent advances in scientific computing and is easily accessible for a general covariance function, via a simple numerical interface. The work offers also analytical results that explain the effectiveness of the implemented methodology and elaborates its utilization for non-Gaussian processes.