Positive Probability Research Articles

Annihilating Branching Brownian Motion

Abstract We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.

Dynamic analysis of HIV infection model with CTL immune response and cell-to-cell transmission

HIV infection is still a serious worldwide public health problem. During the early stage of HIV infection, the number of infected cells and viruses are extremely low and the process of infection is stochastic. In this paper, we use a stochastic model consisting of continuous-time Markov chain to investigate CTL immune response and two modes of infection (viral transmission and cellular transmission). A multitype branching process is used to approximate the probability of clearance and outbreak of HIV infection near the infection-free equilibrium. In addition, we compare the dynamics of the deterministic model with the results of the stochastic model, and the differences are as follows: (1) when R0>1, the deterministic model shows HIV infection outbreak, while the stochastic model indicates a positive probability of HIV infection elimination; (2) the initial number of infected cells and viruses have no effect on the dynamics of the deterministic model, whereas the dynamics of the stochastic model are highly dependent on the initial sizes and cannot be ignored.

Controlled-Release Electrochemiluminescence Biosensor with Strong Self-On Effect by a Multiple Signal Amplification Strategy for Trace Detection of Prostate-Specific Antigen.

The enhancement of sensitivity in biological analysis detection can reduce the probability of false positives of the biosensor. In this work, a novel self-on controlled-release electrochemiluminescence (CRE) biosensor was designed by multiple signal amplification and framework-enhanced stability strategies. As a result, the changes of the ECL signal were enhanced before and after the controlled-release process, achieving sensitive detection of prostate-specific antigen (PSA). Specifically, for one thing, Fe3O4@CeO2-NH2 with two paths for enhancing the generation of coreactant radicals was used as the coreaction accelerator to boost ECL performance. For another, due to the framework stability, zeolitic imidazolate framework-8-NH2 (ZIF-8-NH2) was combined with luminol to make the ECL signal more stable. Based on these strategies, the constructed CRE biosensor showed a strong self-on effect in the presence of PSA and high sensitivity in a series of tests. The detection range and limit of detection (LOD) were 5 fg/mL to 10 ng/mL and 2.8 fg/mL (S/N = 3), respectively, providing a feasible approach for clinical detection of PSA.

Validation of a Method for Surveillance of Nanoparticles in Mussels Using Single Particle Inductively Coupled Plasma Mass Spectrometry.

Determining the concentration of nanoparticles in marine organisms is important for evaluating their environmental impact and to assess potential food safety risks to human health. The current work aimed at developing an in-house method based on single particle inductively coupled plasma mass spectrometry suitable for surveillance of nanoparticles in mussels. A new low-cost and simple protease mixture was utilized for sample digestion, and a novel open-source data processing was used, establishing detection limits on a statistical basis using false positive and false negative probabilities. The method was validated for 30 and 60 nm gold nanoparticles spiked to mussels as a proxy for seafood. Recoveries were 76-77% for particle mass concentration and 94-101% for particle number concentration. Intermediate precision was 8-9% for particle mass concentration and 7-8% for particle number concentration. Detection limits for size was 18 nm and for concentration 1.7 ng/g and 4.2 x 105 particles/g mussel tissue. The performance characteristics of the method were satisfying compared with numeric Codex criteria. Further, the method was applied to titanium-, chromium- and copper-based particles in mussels. The method demonstrates a new practical and cost-effective sample treatment and streamlined, transparent and reproducible data treatment for the routine surveillance of NPs in mussels.

Embeddings of metric Boolean algebras in [formula omitted]

A Boolean algebra A equipped with a (finitely-additive) positive probability measure m can be turned into a metric space (A,dm), where dm(a,b)=m((a∧¬b)∨(¬a∧b)), for any a,b∈A, sometimes referred to as metric Boolean algebra. In this paper, we study under which conditions the space of atoms of a finite metric Boolean algebra can be isometrically embedded in RN (for a certain N) equipped with the Euclidean metric. In particular, we characterize the topology of the positive measures over a finite algebra A such that the metric space (At(A),dm) embeds isometrically in RN (with the Euclidean metric).

Grafite: Taming Adversarial Queries with Optimal Range Filters

Range filters allow checking whether a query range intersects a given set of keys with a chance of returning a false positive answer, thus generalising the functionality of Bloom filters from point to range queries. Existing practical range filters have addressed this problem heuristically, resulting in high false positive rates and query times when dealing with adversarial inputs, such as in the common scenario where queries are correlated with the keys. We introduce Grafite, a novel range filter that solves these issues with a simple design and clear theoretical guarantees that hold regardless of the input data and query distribution: given a fixed space budget of B bits per key, the query time is O(1), and the false positive probability is upper bounded by l/2B-2, where l is the query range size. Our experimental evaluation shows that Grafite is the only range filter to date to achieve robust and predictable false positive rates across all combinations of datasets, query workloads, and range sizes, while providing faster queries and construction times, and dominating all competitors in the case of correlated queries. As a further contribution, we introduce a very simple heuristic range filter whose performance on uncorrelated queries is very close to or better than the one achieved by the best heuristic range filters proposed in the literature so far.

Make it 'til you fake it

We study the dynamics of fraud and trust in a continuous-time reputation game. The principal wishes to approve a real project and reject a fake. The agent is either an ethical type that produces a real project, or a strategic type that also can produce a fake. Producing a real project takes an uncertain amount of time, while a fake can be created instantaneously at some cost. The unique equilibrium features an initial phase of doubt, during which the strategic agent randomly fakes and the principal randomly approves. Only submissions that arrive after the phase of doubt are beneficial to the principal. We investigate three variants of the model that mitigate this problem. With full commitment, the principal incentivizes the strategic agent to fake at one specific time and commits to approve. Though the principal knows that earlier arrivals are real, she commits to reject them with positive probability. When she can delegate authority, the principal benefits by transferring it to a proxy who is more cautious than she is. When the principal can conduct a costly test prior to her approval decision, the principal also benefits. The equilibrium testing probability may be non-monotonic over time, first increasing, then decreasing.

Long‐time existence of Brownian motion on configurations of two landmarks

AbstractWe study Brownian motion on the space of distinct landmarks in , considered as a homogeneous space with a Riemannian metric inherited from a right‐invariant metric on the diffeomorphism group. As of yet, there is no proof of long‐time existence of this process, despite its fundamental importance in statistical shape analysis, where it is used to model stochastic shape evolutions. We make some first progress in this direction by providing a full classification of long‐time existence for configurations of exactly two landmarks, governed by a radial kernel. For low‐order Sobolev kernels, we show that the landmarks collide with positive probability in finite time, whilst for higher‐order Sobolev and Gaussian kernels, the landmark Brownian motion exists for all times. We illustrate our theoretical results by numerical simulations.

One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II

Continuing our earlier work in Nam et al. (One-step replica symmetry breaking of random regular NAE-SAT I, arXiv:2011.14270, 2020), we study the random regular k-nae-sat model in the condensation regime. In Nam et al. (2020), the (1rsb) properties of the model were established with positive probability. In this paper, we improve the result to probability arbitrarily close to one. To do so, we introduce a new framework which is the synthesis of two approaches: the small subgraph conditioning and a variance decomposition technique using Doob martingales and discrete Fourier analysis. The main challenge is a delicate integration of the two methods to overcome the difficulty arising from applying the moment method to an unbounded state space.

Stopping times occurring simultaneously

Stopping times are used in applications to model random arrivals. A standard assumption in many models is that they are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. We use a modified Cox construction along with the bivariate exponential introduced by Marshall and Olkin (1967) to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We show that our initial construction only allows for positive dependence between stopping times, but we also propose a joint distribution that allows for negative dependence while preserving the property of non-zero probability of equality. We indicate applications to modeling COVID-19 contagion (and epidemics in general), civil engineering, and to credit risk.

A meta-analysis on the diagnostic utility of ultrasound in pediatric distal forearm fractures.

Pediatric distal forearm fractures, comprising 30% of musculoskeletal injuries in children, are conventionally diagnosed using radiography. Ultrasound has emerged as a safer diagnostic tool, eliminating ionizing radiation, enabling bedside examinations with real-time imaging, and proving effective in non-hospital settings. The objective of this study is to evaluate the diagnostic efficacy of ultrasound for detecting distal forearm fractures in the pediatric population. A systematic review and meta-analysis were conducted through a comprehensive literature search in PubMed, Scopus, Web of Science, and Embase databases until October 1, 2023, following established guidelines. Eligible studies, reporting diagnostic accuracy measures of ultrasound in pediatric patients with distal forearm fractures, were included. Relevant data elements were extracted, and data analysis was performed. The analysis included 14 studies with 1377 patients, revealing pooled sensitivity and specificity of 94.5 (95% CI 92.7-95.9) and 93.5 (95% CI 89.6-96.0), respectively. Considering pre-test probabilities of 25%, 50%, and 75% for pediatric distal forearm fractures, positive post-test probabilities were 83%, 44%, and 98%, while negative post-test probabilities were 2%, 6%, and 15%, respectively. The bivariate model indicated significantly higher diagnostic accuracy in the subgroup with trained ultrasound performers vs. untrained performers (p = 0.03). Furthermore, diagnostic accuracy was significantly higher in the subgroup examining radius fractures vs. ulna fractures (p < 0.001), while no significant differences were observed between 4-view and 6-view ultrasound subgroups or between radiologist ultrasound interpreters and non-radiologist interpreters. This study highlighted ultrasound's reliability in detecting pediatric distal forearm fractures, emphasizing the crucial role of expertise in precisely confirming fractures through ultrasound examinations.

Strategic disclosure with reputational concerns

I study a strategic disclosure model wherein an uninformed decision-maker (DM) consults an expert of uncertain types regarding the state before acting. The expert may be an honest type, who is committed to reporting the truth; or a strategic type, whose payoff increases in the DM’s action independent of the state and, thus, strategically discloses information to facilitate his agenda while also valuing a reputation for honesty. We find that if the expert fails to obtain information with positive probability, a monotone equilibrium exists that involves an interval wherein the strategic expert adopts a mixed strategy for disclosure, in contrast to a simple cutoff rule that cannot be sustained in equilibrium. The value that the strategic expert attaches to reputation serves as a commitment device to promote disclosure, as does the higher probability that the state is observed, whereas an honest expert’s greater presence may harm the strategic expert’s disclosure incentive.

Assessment of the diagnostic performance of intradermal tuberculin test and post-mortem inspection for the diagnosis of bovine tuberculosis according to WOAH guidelines

Bovine tuberculosis (bTB) constitutes a global challenge for public and animal health with still some deficiencies regarding its diagnosis. This study aimed to estimate the accuracy of the single intradermal tuberculin test (SIT) and post-mortem inspection for different diagnostic objectives following WOAH guidelines. Tissue samples from 59 microbiological culture/PCR-positive and 58 microbiological culture/PCR-negative cattle were evaluated. The diagnostic sensitivity and specificity, the positive and negative probability indices as well as the positive and negative predictive values (PPV and NPV) of each technique were estimated for different pretest probabilities. The SIT with strict interpretation demonstrated moderate precision in confirming the absence of infection in populations historically free of bTB, with a 12.1% rate of false positives, but also detecting positive animals in the early stage of the eradication programs, with a 13.6% rate of false negatives. The diagnostic performance for ruling out bTB was notably high (NPV > 90%) in animals with a pre-test probability (PTP) below 42%. Post-mortem inspection constituted an interesting alternative tool to confirm suspected and positive cases for SIT, particularly in areas with bTB prevalence exceeding 19%, where implementing SIT and eradication measures may be impractical. In these areas, the likelihood that animals with tuberculosis-like lesions are affected by the disease surpasses 90%. Similarly, in herds with a PTP below 25%, the absence of bTB could be confidently ruled out with over 90% certainty. These findings highlight the effectiveness of SIT and post-mortem inspection as valuable techniques for current eradication programs and controlling bTB in high-prevalence areas where molecular techniques may not be feasible.

Diagnostic performance of endoscopy and MRI in identifying true response among patients with rectal cancer treated with total neoadjuvant therapy and selective watch and wait or TME.

28 Background: The success of a watch-and-wait (WW) strategy for rectal cancer relies on restaging endoscopy and MRI to correctly identify a true response (TR) to neoadjuvant treatment. This secondary analysis of the OPRA trial is the first study to evaluate the restaging assessment’s diagnostic performance in a large cohort of WW patients. Methods: In the OPRA trial, patients with stage II/III rectal cancer were treated with total neoadjuvant therapy (TNT) and restaged with endoscopy and MRI 8±4 weeks post-treatment. Patients with a clinical complete (cCR) or near complete (nCR) response were offered WW; patients with an incomplete clinical response were recommended for total mesorectal excision. Diagnostic parameters, including accuracy, sensitivity, specificity, positive and negative predictive values, were calculated using TR as the reference standard. TR was defined as pathologic complete response for patients treated with TME or sustained cCR for ≥2 years for patients on WW. Contingency tables were prepared for two approaches: one considering either cCR or nCR positive for a TR, and one considering cCR as the only response grade positive for a TR. Results: Of the 304 patients restaged after completing TNT, 265 (87.2%) with ≥2 years of follow-up data available were included. Restaging endoscopy outperformed MRI across all parameters. Accuracy improved minimally to 66% when both modalities agreed on a cCR or nCR (Table). Restricting a positive result to cCR resulted in higher specificity, lower sensitivity, and higher accuracy (75%) (Table 1B). The positive posttest probability that a patient with a cCR had a TR was 81%, while the negative posttest probability that a patient with a non-cCR had a TR was 30%. Conclusions: Restaging endoscopy outperforms MRI in predicting TR, but the assessment’s overall accuracy even when both tests are combined remains suboptimal. Our results highlight the challenge of recognizing TR using subjective restaging exams. Opportunities to improve diagnostic accuracy include machine learning and radiomics, which have the potential to aid clinicians in identifying true responders. [Table: see text]

Random Dirichlet series with [formula omitted]-stable coefficients

Let P be a set of non-negative real numbers, we consider a class of random Dirichlet series D(s)=∑p∈Pξpps with symmetric α-stable (0<α⩽2) coefficients. Real zero point problem of D is studied firstly. We prove that, if Z(τz)<∞, then with a positive probability there are no real zero points in the interval [τz/α,∞), while if Z(τz)=∞, for any ɛ>0, almost surely D has infinite number of real zeros in the interval s=(τz/α,τz/α+ɛ). Here, Z(s)=∑p∈P1ps and τz is its abscissa of convergence (see Section 1). In the proof, we find that lim sups→1/α+D(s)=∞ almost surely under the condition Z(τz)=∞. Finally, to get more asymptotic information for D(s), under P=N, some asymptotic properties for D(s) compared with Z(αs) are explored as s→1/α+.

“They don't let us speak”: Gender, collegiality, and interruptions in deliberations in the Brazilian Supreme Court

AbstractIn this paper, we examine a database containing court rulings and debates (acórdãos) of the Brazilian Supreme Court (“STF”) spanning from 1999 to 2018. Our objective is to analyze the relationship between gender and how judges behave when interacting with each other. Specifically, we investigate whether female judges are more likely to be interrupted by their colleagues during oral debates. Our data are built on real‐time public interactions between the judges, as recorded in the Court's transcripts. The results show that female STF judges are interrupted more often than their male counterparts. While male judges display no specific effects, all three female judges in our data display a very significant and positive probability of being interrupted, as compared to their male colleagues participating in the same deliberations. These results show that, even in institutions designed to protect rights of political minorities, including women, gender dynamics, stereotypes and hierarchies can affect the functioning of courts in visible ways, with potential impacts on the rest of the judiciary and the legal profession. They also suggest that merely increasing the number of female judges, without addressing underlying gender dynamics and procedural rules in the judicial decision‐making process, is insufficient to tackle the disadvantages women face within those institutions.

Population-Based Validation of the MIA and MSKCC Tools for Predicting Sentinel Lymph Node Status

Patients with melanoma are selected for sentinel lymph node biopsy (SLNB) based on their risk of a positive SLN. To improve selection, the Memorial Sloan Kettering Cancer Center (MSKCC) and Melanoma Institute Australia (MIA) developed predictive models, but the utility of these models remains to be tested. To determine the clinical utility of the MIA and MSKCC models. This was a population-based comparative effectiveness research study including 10 089 consecutive patients with cutaneous melanoma undergoing SLNB from the Swedish Melanoma Registry from January 2007 to December 2021. Data were analyzed from May to August 2023. The predicted probability of SLN positivity was calculated using the MSKCC model and a limited MIA model (using mitotic rate as absent/present instead of count/mm2 and excluding the optional variable lymphovascular invasion) for each patient. The operating characteristics of the models were assessed and compared. The clinical utility of each model was assessed using decision curve analysis and compared with a strategy of performing SLNB on all patients. Among 10 089 included patients, the median (IQR) age was 64.0 (52.0-73.0) years, and 5340 (52.9%) were male. The median Breslow thickness was 1.8 mm, and 1802 patients (17.9%) had a positive SLN. Both models were well calibrated across the full range of predicted probabilities and had similar external area under the receiver operating characteristic curves (AUC; MSKCC: 70.8%; 95% CI, 69.5-72.1 and limited MIA: 69.7%; 95% CI, 68.4-71.1). At a risk threshold of 5%, decision curve analysis indicated no added net benefit for either model compared to performing SLNB for all patients. At risk thresholds of 10% or higher, both models added net benefit compared to SLNB for all patients. The greatest benefit was observed in patients with T2 melanomas using a threshold of 10%; in that setting, the use of the nomograms led to a net reduction of 8 avoidable SLNBs per 100 patients for the MSKCC nomogram and 7 per 100 patients for the limited MIA nomogram compared to a strategy of SLNB for all. This study confirmed the statistical performance of both the MSKCC and limited MIA models in a large, nationally representative data set. However, decision curve analysis demonstrated that using the models only improved selection for SLNB compared to biopsy in all patients when a risk threshold of at least 7% was used, with the greatest benefit seen for T2 melanomas at a threshold of 10%. Care should be taken when using these nomograms to guide selection for SLNB at the lowest thresholds.

Mixture independence foundations for expected utility

An alternative preference foundation for expected utility is provided. Our segregated approach considers four logically independent implications of the classic von Neumann–Morgenstern independence axiom. The monotonicity principle is, for a transitive relation, equivalent to monotonicity with respect to first-order stochastic dominance. Rank-dependent separability is similar to the comonotonic sure-thing principle used in the ambiguity literature. The remaining two properties are weak formulations of the independence principle which invoke the latter only for probability mixtures with the extreme, that is the best, respectively, the worst outcome. These four implications of independence, together with completeness, transitivity and continuity of a preference relation, characterize expected utility. Furthermore, if rank-dependent separability is dropped, expected utility still holds on each subset of three-outcomes lotteries that give positive probability to both the best and the worst outcomes.

SERS-Temperature Dual-Mode T-type Lateral Flow Strip for Accurate Detection of Free and Total Prostate-Specific Antigens in Blood.

Accurate point-of-care (POC) analysis of cancer markers is the essence in the comprehensive early screening and treatment of cancer. Dual-mode synchronous detection is one of the effective approaches to reduce the probability of false negatives or false positives. As a result, this can greatly improve the accuracy of diagnosis. In this work, a surface-enhanced Raman scattering (SERS)-temperature dual-mode T-type lateral flow strip was fabricated to direct and simultaneous POC detection of total and free prostate-specific antigens (t-PSA and f-PSA) in blood. With the advantage of high stability of T-type lateral flow strip and simultaneous acquirement of assay results for t-PSA and f:t PSA ratio, the proposed method has high accuracy in the diagnosis of prostate cancer, especially in the diagnostic gray zone between 4.0 and 10.0 ng/mL. The SERS-temperature dual-signal has a good linear correlation with either f-PSA or t-PSA. To evaluate the clinical diagnostic performance of the proposed method, spiked human serum samples and the whole blood sample were analyzed. The assay results showed good recovery, and compared with traditional electrochemiluminescence immunoassay (ECLIA) method (t-PSA: 43.151; f/t ratio: 0.08), the results obtained by the proposed method were similar (t-PSA: 40.15 (SERS), 36.21 (temperature); f/t ratio: 0.08 (SERS), 0.08 (temperature), but the detection time (15 min) and cost ($0.05) had been greatly reduced. Therefore, the proposed SERS-temperature synchronous dual-mode T-type lateral flow strip has a strong application potential in the field of accurate large-scale diagnostics of prostate cancer on-site by simultaneous POC detection of t-PSA and f-PSA in blood.

Evaluation of antihypertensive activity and molecular docking analysis of Padina boergesenii extract

IntroductionAntihypertensive drugs that are chemically synthesized usually tend to initiate different health complications. The quest for bioactive molecules to create novel medicines has focused on Marine resources like seaweeds. These molecules can furnish a positive probability for patients to gain benefits from these natural substances. MethodsThis study aims to identify phytoconstituents present in brown seaweed-Padina boergesenii. Five different solvents were used to prepare extracts and their antioxidant activity as well as antihypertensive activity was evaluated. Phytoconstituents were identified using LC-MS/MS, and subjected to molecular interaction against ACE enzyme. ResultsThe 70% ethanolic extract exhibited the highest total phenolic content (TPC), significant radical scavenging activity and concentration dependent Angiotensin Converting Enzyme (ACE) inhibition activity. LC-MS/MS analysis confirmed the presence of bioactive compounds from which 7,8 dihydroxycoumarin had the highest affinity against ACE enzyme in molecular docking study. ConclusionThese findings advocate that Padina boergesenii can be a potential source for developing novel antihypertensive therapeutic drug(s) and could pave the way for evolving effective and safe remedies from natural resources.