To quantify the relative contribution of radiologists and urologists to variability in clinically significant prostate cancer (CSPC) detection across multiparametric magnetic resonance imaging (mpMRI)-guided prostate fusion biopsies and to determine whether this differed across Prostate Imaging-Reporting And Data System (PI-RADS) categories. We analysed biopsy-naïve men within the Michigan Urological Surgery Improvement Collaborative (MUSIC) who underwent fusion biopsy between August 2017 and November 2021. The primary outcome was the proportion of variance in CSPC detection (Gleason score ≥3 + 4) at targeted regions of interest that was explained by individual urologists and radiologists. We used generalised linear mixed-effects models to partition variance and estimate intraclass correlation coefficients (ICCs) for radiologist- and urologist-level effects for PI-RADS score 3-5 lesions. We calculated the median odds ratio (MOR) to quantify the expected difference in odds of CSPC detection when comparing a randomly selected higher- vs lower-detecting provider from the same distribution. Among 1544 men with 2045 targeted lesions, mpMRIs were interpreted by 115 radiologists and biopsies performed by 86 urologists. For PI-RADS score 3 lesions, urologists (ICC = 0.15, MOR = 2.07) accounted for greater variance in CSPC detection than radiologists (ICC = 0.07, MOR = 1.61). For PI-RADS score 4, both urologist (ICC = 0.05, MOR = 1.49) and radiologist (ICC = 0.07, MOR = 1.61) contributed modestly. For PI-RADS score 5, radiologists (ICC = 0.17, MOR = 2.19) explained a larger proportion of variance than urologists (ICC = 0.01, MOR = 1.19), suggesting individual radiologists meaningfully impact CSPC detection of high-risk lesions. For PI-RADS score 3 lesions, the specific urologist performing the biopsy was a strong source of variation, while for PI-RADS score 5 lesions, the radiologist had greater influence on CSPC detection rates. Optimising MRI acquisition and interpretation, ensuring accurate fusion registration, and improving biopsy accuracy are critical to improving diagnostic consistency.

To investigate performance, recovery, sleep, nocturnal physiology, ovarian hormone concentrations, and menstrual cycle symptoms within and between menstrual cycle phases and establish within-phase reliability of these measures. Twenty naturally cycling, trained female participants (age 27 ± 5 yr) completed a repeated measures study design. Serum estradiol and progesterone concentrations, countermovement jumps, isometric mid-thigh pulls, a repeated 5 km cycle time trial, and two nights of sleep architecture were measured in phases one, three, and four of two menstrual cycles. Sleep and wake measures from activity monitoring, nocturnal heart rate (HR) measures from the Oura Ring, and menstrual cycle symptoms were monitored daily. Statistical analyses included linear mixed models and reliability measures. Estradiol concentrations were significantly lower in phase one versus three, one versus four, and three versus four ( P < 0.001 to 0.04) in both menstrual cycles. Progesterone concentrations were significantly lower in phase one versus four, and three versus four ( P < 0.001) in both menstrual cycles. Symptoms were significantly higher in phase one versus three and four ( P < 0.001) in cycle one only. No significant differences between phases were found for performance, recovery, and sleep in either cycle, except for the nonrapid eye movement stage three (N3%) sleep in cycle two. Nocturnal average HR was significantly lower ( P < 0.001) and HR variability higher ( P < 0.001) in phase one versus four in both cycles. Ovarian hormone concentrations were highly variable within each phase (coefficients of variance 28%-95%), while performance and recovery demonstrated minimal variability in both cycles. Performance, recovery, and sleep in trained female participants remained consistent despite ovarian hormone fluctuations. Consequently, practitioners should test athletes when convenient, using accurate and reliable assessments rather than synchronizing testing with specific menstrual cycle phases.

A 28-day study was conducted to examine the effects of photoperiods with multiple light/dark cycles on growth performance and oxidative stress for largemouth bass (Micropterus salmoides) larvae in recirculating aquaculture systems (RAS). Larvae fish were exposed to four different photoperiods [light/dark (L:D), h] as follows: 6L:18D; 12L:12D; 18L:6D and 24L:0D. The feeding number was 8 times a day. The light duration of each treatment was 45min, 90min, 135min and 180min respectively in one light/dark cycle (feeding interval) of 180min. A total of six thousand fish (0.5229 ± 0.0180cm, 0.0021 ± 0.0002g) were randomly kept in the 12 cages (4 treatments × 3 replicates × 500 individuals). The results showed that the body weight, weight gain rate (WGR), specific growth rate (SGR), thermal growth coefficient (TGC), Fulton's condition factor (K) and mRNA expressions of growth hormone (gh) and insulin-like growth factor 1 (igf-1) generally increased with the extension of photoperiods, and they were highest in the 24L:0D treatment and were second in the 18L:6D treatment. The variation coefficients for body length (CVfl) and body weight (CVfw) were lowest in 18L:6D treatment. There was no significant difference in survival rate (SR) among four treatments. The levels of Malonaldehyde (MDA), total antioxidant capacity (T-AOC) and mRNA expressions of heat shock protein 70 (hsp70), corticotropin-releasing factor receptor 1 (crfr1) and caspase-3 (cas-3) were all significantly higher in 6L:18D and 24L:0D treatments than those of 18L:6D and 12L:12D treatments. This indicated the photoperiods of 6L:18D and 24L:0D regimes induced an oxidative stress response in the larvae when the photoperiods were excessively compressed and extended. Overall, 18L:6D treatment is the optimal light regime for largemouth bass larvae culture in RAS. However, experimental comparisons between cyclic light/dark and continuous regimes are warranted to further evaluate animal welfare implications and inform aquaculture practice.

Shearwave elastography (SWE) to detect hyperglycaemic changes in the placenta (a pilot feasibility study).

Conventional lateral flow immunoassays (LFIAs) suffer from limited sensitivity due to weak optical signals from colloidal gold, random antibody orientation, and inconsistencies in nanoprobe synthesis. To address these challenges, we introduce a dual-enhancement strategy integrating gold-decorated ferritin nanocages (HFn@Au) with SpyTag/SpyCatcher-mediated oriented antibody immobilization. Engineered ferritin displaying SpyTag peptides on its surface served as a precise template for the controlled nucleation and growth of gold nanoclusters, resulting in highly uniform core-shell nanostructures (PDI = 0.242; size variation coefficient = 12.56%) with significantly amplified optical intensity. Importantly, this deposition process preserved the functionality of the SpyTag sites. Subsequent incubation with SpyCatcher-fused antibodies enabled spontaneous isopeptide bond formation, ensuring site-specific and covalent antibody conjugation. This oriented immobilization enhanced the effective antigen-binding capacity by approximately 8-fold compared to random adsorption. Using human chorionic gonadotropin (hCG) as a model analyte, the optimized LFIA achieved a limit of detection (LOD) of 0.5 mIU per mL, representing a 50-fold sensitivity improvement over commercial gold nanoparticle-based strips (LOD ≈ 25 mIU per mL). The assay demonstrated acceptable linearity from 2.5 to 20 mIU per mL (R2 = 0.956) and high reliability in urine matrices, with spike-recovery rates between 91.70% and 108.30%. This synergistic strategy provides a versatile and powerful method for dramatically enhancing the sensitivity of point-of-care diagnostics, representing an encouraging step toward practical real-sample application.

ABSTRACTPlant distribution correlates with climate change, especially in mountain flora. Using an optimized MaxEnt model and the latest WorldClim 2.1 bioclimatic data, this study identified the key environmental determinants of habitat suitability and projected the current and future distribution patterns of seven Meconopsis spp. in China under various climate change scenarios. Results reveal that the primary environmental variables shaping the distribution are isothermal (bio3), seasonal variation coefficient of temperature (bio4), and elevation. Seven taxa were concentrated in southwestern China, with suitable habitats encompassing 1.3% to 10.1% of the land area in China. Under future climate scenarios, M. lyrata is expected to experience a decline in habitat suitability, and other species showed mixed responses. Given the limited extent of suitable habitats for most Meconopsis species in China, ex‐situ conservation—particularly through initiatives spearheaded by national botanical research institutions—should prioritize domestication and conservation efforts to safeguard genetic diversity.

Test-retest reliability of dopaminergic fPET and fMRI measures during reward processing.

Youth-onset type 2 diabetes and obesity are rising public health burdens. While newer type 2 diabetes medications lower HbA1c, their impact on paediatric weight loss is inconsistent. In contrast, bariatric surgery improves glycemia and weight in youth and adults, though glycemia post-vertical sleeve gastrectomy (VSG), now the predominant bariatric surgery in youth, remains unstudied in youth-onset type 2 diabetes. We aimed to assess immediate post-VSG glycemic patterns using continuous glucose monitoring (CGM) in adolescents with type 2 diabetes. In the Surgical or Medical Treatment for Paediatric Type 2 Diabetes (ST2OMP) study, 73 adolescents with type 2 diabetes underwent 14 days of CGM monitoring: 33 participants beginning in the 1-2 days post-VSG (mean age 17.6 years, 67% female, HbA1c 7.2%, BMI 50.0 kg/m2) and 40 participants receiving advanced medical therapy (AMT) (mean age 16.9 years, 53% female, HbA1c 7.8%, BMI 42.2 kg/m2). CGM analyses included glucose management indicator (GMI), time in range, coefficient of variability, standard deviation, mean amplitude glycemic excursion, percent > 140, 180, and 200, percent < 70 and 60 mg/dL, 7 a.m., and midnight-6 a.m. Mean glucose was 84.3 ± 23.4 in the post-VSG group versus 149.8 ± 78.8 mg/dL in the AMT group (p < 0.001). Mean CGM GMI was normal (5.3%, 34 mmol/mol) post-VSG versus in the diabetes range (6.9%, 52 nmol/mol) with AMT (p < 0.001). VSG participants spent more time < 70 mg/dL, 55 mg/dL, and 45 mg/dL (all p < 0.01). After BMI adjustment, preoperative HbA1c predicted postoperative glucose metrics. Adolescents with type 2 diabetes experience early glycemic normalization post-VSG, even before major weight loss.

Neurochemical levels measured by brain MR spectroscopy (MRS) have been proposed as endpoints for clinical trials in early-stage spinocerebellar ataxia (SCA) trials. We tested their trial-readiness by quantifying neurochemicals in three affected brain regions in early-stage cohorts of SCA2 and SCA3, examining their reproducibility in both patients and controls in a multisite/multivendor setting, and determining if the same neurochemical outcomes can be used as endpoints for different SCA genotypes. Seventy-two participants (18 SCA2, mean Scale for the Assessment and Rating of Ataxia (SARA) = 9 +/- 5; 25 SCA3, mean SARA = 10 +/- 6; 29 controls) underwent 3 T scans at four sites using scanners from two vendors and a harmonized MRS protocol. Scans were performed twice with a maximum 2-week interval. We measured neurochemical concentrations in the cerebellum, pons, and putamen, and assessed their within- and between-site reproducibility and associations with clinician- and patient-reported outcomes. Test-retest coefficients of variance were comparable across sites and vendors, but concentration estimates had to be adjusted for sites to account for small vendor-based biases. Total N-acetylaspartate (tNAA) and glutamate were lower, and myo-inositol (mI) and total creatine (tCr) were higher in the cerebellum and pons in both SCAs vs. controls. Pontine tNAA and mI, and cerebellar tNAA, mI, and glutamate levels were significantly different between SCA2 and SCA3, with strong effect sizes (|Cohen's d| = 1.1-2.1). The tNAA/tCr ratio had the strongest associations with clinical outcomes (|r| ≥ 0.5), with stronger associations in the cerebellum for SCA2 and in the pons for SCA3. These data support the use of tNAA and its ratios in a genotype-specific manner in early-stage SCA2 and SCA3 trials in the multisite/multivendor setting.

The increasing demand for future digital technologies and high-temperature neuromorphic hardware will rely on non-volatile behavior and power efficiency. High-temperature devices are crucial for space exploration and function in severe environments, such as industrial units. Two-dimensional transition metal dichalcogenides (TMDs) are known for their strong mechanical properties, which make them frontrunners for next-generation device fabrication. This paper presents an Ag/WS2/W memristive device deposited onto a silicon substrate utilizing a direct current (DC) magnetron sputtering technique that can operate at high temperatures. The device displays steady and reliable gradual resistive switching characteristics with low set/reset switching voltages (+0.65 V/-0.55 V). Device also exhibits an excellent electrical endurance (>2500 cycles), retention time (>104 s), and good cycle-to-cycle variability with low variation coefficient, confirming its consistency and robustness. Temperature-dependent current-voltage measurements were utilized to investigate the conduction behavior of the developed memristive device. The measured electrical characteristics highlighted a thermally assisted conduction process, thereby justifying the proposed switching model. Furthermore, the memristor device emulated fundamental synaptic plasticity functionalities, including long-term potentiation (LTP), long-term depression (LTD), paired-pulse facilitation (PPF), and paired-pulse depression (PPD). This study highlights 2D WS2 as an emerging material that can serve effectively as an artificial synapse and also maintains steady operation at elevated temperatures. These findings pave the way for the realization of state-of-the-art neuromorphic computing platforms.

Age-related neuromuscular dysfunction is widely recognized; however, the extent to which aging is accompanied by motor neuron (MN) loss remains underexplored. This review evaluates evidence for MN loss with aging across species and anatomical motor pools. We synthesize PUBMED studies in humans, non-human primates, rats and mice within the spinal cord and brainstem. Attention was given to the methodological approach used to quantify MNs and categorized based on what MNs were quantified (specific pools, vertebral levels, lateral motor columns). Methods were assessed qualitatively, based on stereological and non-stereological density counting approaches, and the staining techniques identified as optimal or suboptimal by defined criteria. To facilitate cross-study comparison we conducted quantitative assessments including: coefficients of variance, percentage differences between groups and standardized effect sizes calculated with Cohen's d. Across species and anatomical regions, the overall literature supports the presence of age-related MN loss. Evidence is strongest in studies using robust counting approaches such as stereology, and appropriate MN markers. As age-related MN degeneration is more heavily investigated and becomes a locus of intervention, future work must employ rigorous methodological standards to accurately determine the extent, regional specificity, and functional consequence of aging MN loss.

In many areas of psychology, researchers are interested in studying whether intraindividual variability (IIV) is predictive of behavioral and health outcomes after controlling for the intraindividual mean. To the end, IIV indicators such as the observed intraindividual variance (OIVAR) or the observed intraindividual standard deviation (OISD) are often modeled as a predictor in regular regression analysis. However, OIVAR and OISD have been found to have a low-reliability problem, especially when the number of occasions is small. In this study, we analytically examined statistical features (mean and variance) of OIVAR and OISD. The results revealed that when measurement errors exist, regular regression can yield (a) more accurate results for the coefficient of intraindividual variance (IVAR) but (b) worse results for the coefficient of intraindividual standard deviation (ISD) when the number of occasions increases. Furthermore, we compared the performance of alternative modeling approaches, including the time-parceling, single indicator latent variable, and Bayesian variability modeling approaches, to that of regular regression for modeling IVAR or ISD as a predictor. Simulation results were consistent with the analytical results and further suggested that our proposed (a) time-parceling with bootstrapping and (b) Bayesian variability modeling approaches performed well and better than regression for modeling IVAR as a predictor. When measurement errors exist, only the proposed Bayesian variability modeling approach performed well for modeling ISD as a predictor. Implications of the results and recommendations were discussed. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Arterial pulse harmonic alterations: a novel biomarker linking vascular dysfunction to prefrailty.

Microscopic characteristics and fractal Representation of limestone reservoirs in the Taiyuan Formation, Ordos Basin

The triglyceride-glucose (TyG) index is a simple surrogate marker for insulin resistance (IR), but its longitudinal stability and clinical predictive value in patients with cancer remain poorly understood. To evaluate whether cancer and anti-tumor therapies affect the longitudinal stability of the TyG index over 24 months and to identify its core influencing factors. This retrospective study analyzed 538 cancer patients from a single-center database (2015-2020) who completed five TyG index measurements over 24 months. Longitudinal stability was quantified using repeated measures analysis of variance (RM-ANOVA) and intraclass correlation coefficients (ICC). Binary logistic regression models were employed to explore factors associated with different TyG levels. A longitudinal K-means clustering algorithm was used to identify trajectory differences, and multivariable logistic regression models determined the independent predictive factors. The TyG index demonstrated excellent longitudinal stability over 24 months (F = 5.38, P < 0.001; average ICC = 0.890; Pearson r = 0.54-0.71). Binary logistic regression analysis showed that body mass index (BMI) was the core factor independently associated with a high TyG index (Q4 > 8.79). K-means clustering identified three parallel longitudinal trajectories (Stable-Low, Stable-Medium, and Stable-High risk). Multivariable logistic regression models indicated that the high-risk trajectory was significantly associated with BMI (OR = 1.25, 95% CI 1.10-1.41, P < 0.001) and diabetes mellitus, whereas advanced cancer stage (OR = 0.95, 95% CI 0.53-1.70, P = 0.862) and cachexia (OR = 0.90, 95% CI 0.45-1.80, P = 0.767) showed no significant effect. The TyG index in cancer patients exhibited a long-term stable trend over 24 months. Severe IR may represent a metabolic phenotype closely associated with fat accumulation, and it may be independent of catabolic states such as cancer stage and cachexia.

Introduction Toxicologists are often called upon to interpret results of drug testing. Phosphatidylethanol is a biomarker sensitive for ethanol consumption within the previous one to four weeks and is commonly used in monitoring for alcohol abstinence in organ transplant candidates. Phosphatidylethanol is stable in stored units of packed red blood cells and has been shown to create “false positive” or iatrogenically elevated phosphatidylethanol concentrations after blood transfusion. Methods In this prospective observational study, 50 subjects receiving one unit of packed red blood cells transfusion had their pre- and post-transfusion whole blood phosphatidylethanol concentrations measured using whole blood samples in EDTA vacutainers obtained within 24 hours of transfusion. Phosphatidylethanol was measured using liquid chromatography-tandem mass spectrometry with a 15% coefficient of variance. Pre- and post-transfusion hemoglobin and hematocrit were also measured. Results Four (8%) subjects had an increase in phosphatidylethanol from “negative” (<20 ng/mL) to “positive” (>20 ng/mL) after transfusion. Six (12%) total subjects had any increase in phosphatidylethanol concentration beyond the coefficient of variance with a maximum increase of 51 ng/mL. No subjects had a decrease in phosphatidylethanol beyond the coefficient of variance. Discussion This study adds to the evidence that patients receiving blood transfusions may have iatrogenically elevated phosphatidylethanol concentrations, even with a single unit of packed red blood cells. Conclusion Phosphatidylethanol concentrations should be interpreted with caution if a patient has recently received a blood transfusion.

Continuous glucose monitoring (CGM) enables scalable digital phenotyping by capturing detailed daily glucose profiles and has been shown to improve glycaemic control in individuals with type 1 diabetes (T1D). We hypothesized that clustering CGM-derived metrics could identify distinct glycemic phenotypes associated with increased insulin resistance, systemic inflammation, and risk of metabolic derangements, with potential implications for optimization of clinical care. This cross-sectional study applied a hierarchical clustering approach to stratify 75 individuals with T1D based on CGM metrics obtained over 14 days (Libre ProIQ). Clustering was performed using Ward's minimum variance linkage and Euclidean distance on six CGM metrics (average glucose, coefficient of variance, time above range, time below range, time in range, and frequency of low glucose events). The resulting groups, poorly controlled diabetes (PCD) and moderately controlled diabetes (MCD), were compared for insulin resistance markers (estimated glucose disposal rate, eGDR), metabolic dysfunction-associated steatotic liver disease (MASLD) risk markers (fatty liver index, FLI; hepatic steatosis index, HSI), and inflammation and endotoxaemia markers. Compared to MCD, subjects in the PCD group had significantly higher insulin resistance (eGDR: 4.4 vs. 7.3mg/kg/min, p = 0.001), elevated liver enzymes (ALT: 26 vs. 20 U/L, p = 0.005; AST: 28 vs. 23 U/L, p = 0.049), increased MASLD risk markers (HSI: 37 vs. 35, p = 0.033; FLI: 29 vs. 17, p = 0.034), and higher systemic inflammation (CRP: 1.82 vs. 0.81mg/L, p = 0.020; lipopolysaccharide-binding protein (LBP): 11.7 vs. 8.4 EU/mL, p = 0.024). Time above range correlated positively with liver and inflammatory markers, while time in range correlated negatively. Mediation analysis suggested that FLI partially mediated the effect of poor glycemic control on inflammation. In this cross-sectional cohort of adults with T1D, poorer CGM-derived glycaemic control was associated with higher systemic inflammation and higher surrogate-marker-defined MASLD risk.

Quantify beta-2 transferrin (B2T)-positivity in the middle ear fluid of patients undergoing pressure equalization tube (PET) placement for recurrent acute otitis media (RAOM) or chronic otitis media with effusion (COME). Prospective. Tertiary referral center. Eighty-one ears from 60 patients undergoing PET placement. Mean age was 12.1 years. Forty-three ears (60.6% of ears) were male. Forty-five ears (63.4%) had COME. Mean effusion duration was 6.2 months. PET placement. B2T was measured in middle ear aspirates using quantitative ELISA. Ten ears were excluded due to coefficients of variance >20% between duplicate wells, likely from sample viscosity. B2T-positivity rate and quantitative levels. Of 71 ears, 55 (77.5%) were B2T-positive. Compared with B2T-negative ears, B2T-positive ears were more likely to be younger (6.1 vs. 32.9y, P=0.004), have mucoid effusion (70.9% vs. 20.0%, P=0.001), and have RAOM (45.6% vs. 12.5%, P=0.02). Fifty-three of 61 pediatric ears (86.9%) were B2T-positive, compared with 2 of 10 adult ears (20%). B2T-positivity was not associated with gender, effusion duration, or color of aspirate. No patients had chronic otorrhea after PET placement. Although B2T is considered the gold standard to detect cerebrospinal fluid (CSF), our study shows high B2T positivity rates in the middle ear fluid of patients undergoing PET placement for RAOM or COME. B2T may not be specific for CSF leak into the middle ear. Clinicians should exercise caution when interpreting results of B2T testing, particularly in the pediatric population and those with mucoid effusions.

Single-voxel proton magnetic resonance spectroscopy (1H-MRS) is a non-invasive in vivo imaging technique used to quantify the concentration of human brain metabolites. Frequency-selective 1H-MRS techniques reduce spectral complexity and simplify spectral modeling. We introduce a single-shot frequency-selective sequence known as Delays-Alternating-Nutation-Tailored-Excitation-Point-RESolved-Spectroscopy (DANTE-PRESS) and test its precision when measuring glutamate and NAA at 7 Tesla in phantoms and human brain in vivo. DANTE-PRESS was programmed within the software environment of the Siemens Magnetom 7 Tesla MR scanner at the Centre for Functional Metabolic Mapping in London, Ontario. Two scans were obtained on phantoms and in 4 healthy volunteers (20 × 20x20mm3 voxel at the dorsal anterior cingulate cortex) as an in vivo proof-of-concept to refocus glutamate or NAA. DANTE-PRESS preserves the signal of the metabolite of interest while suppressing unwanted signals via a narrow-band frequency-selective refocusing pulse. DANTE-PRESS produces metabolite spectral signatures with J-evolution equivalent to that seen in a PRESS sequence with less than half the echo time. The inter-individual coefficients of variance were low and Cramer-Rao Lower Bounds were less than 5.1% for glutamate and NAA. Future work involving test-retest in vivo study in healthy volunteers to get measurements of glutamate along with other metabolites such as glutathione and GABA.

ABSTRACTRationaleLyon and coworkers demonstrated that multiple random fragmentation events can bias intensity distributions toward smaller terminal fragment ions. With any high‐yield method of dissociation, such as high‐energy collisional activation, this phenomenon can greatly influence the intensity distribution of product ions in MS/MS spectra. Previously, multiple fragmentation events were simulated with computationally intensive stochastic studies. The goal of this work is to provide a mathematical model that explains the results obtained from computational stochastic studies.MethodsWe present a probabilistic model that predicts terminal and internal product ion intensities based on polypeptide size and the number of fragmentation events. This model is validated by demonstrating convergence with the previous stochastic model and described that the intensity trend from smaller fragments to larger fragments follows the probability of multiple fragmentation events on peptide backbone.ResultsUnder the stated assumptions, the analytical expressions formally demonstrate that the “missing middle” is a necessary mathematical consequence of multiple fragmentation events, and they reproduce the stochastic simulation results with exact agreement while reducing computation time from hours to less than 1 s. Our method consistently offers greater accuracy and mathematically proves the mechanistic necessity of “missing middle” phenomenon in top‐down MS. The abundances of fragments from stochastic simulation distribute around the average value calculated by the probability formula within twofold coefficient variance (%CV).ConclusionThe closed‐form probability expressions accurately describe the combinatorial consequences of multiple fragmentation events under the stated assumptions. Because they are computationally inexpensive and differentiable, these expressions could be integrated with sequence‐dependent fragmentation propensities in future machine learning models for MS/MS spectral prediction.