Jashore University of Science and Technology

Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended. We introduce \emph{Bidirectional Provability Fingerprinting} (\bpf{}), a framework that certifies faithfulness by characterizing each candidate through its forward and backward consequence neighborhoods in the ambient theory and matching these against probes derived from the natural-language statement. We further introduce four novel components: (i) \emph{Counterfactual Probe Generation} (\cpg{}), a contrastive procedure that synthesizes probes targeting specific drift directions; (ii) the \emph{Equivalence Spectrum}, a continuous faithfulness score that replaces brittle binary verdicts; (iii) \emph{Adaptive Probe Budget Allocation} (\apba{}), an information-theoretic budget router; and (iv) \emph{Faithfulness-Guided Decoding} (\fgd{}), which uses \bpf{} signals as a reward during autoformalization. We prove a \emph{drift detection theorem} and a \emph{PAC-faithfulness} result establishing that the equivalence class of a natural language statement is learnable from $\mathcal{O}(\log(1/δ)/\varepsilon)$ probes under mild assumptions. We release \driftbench{}, a benchmark of $2{,}183$ NL/Lean~4 pairs with controlled drift labels across six subfields of mathlib4. \bpf{}\,+\,\cpg{} detects $89.6\%$ of drifted formalizations at a $3.0\%$ false-positive rate-against $41.2\%$ for typecheck and $63.3\%$ for LLM-judge baselines, and \fgd{} reduces the rate at which a state-of-the-art autoformalizer emits drifted statements by $47\%$. https://pmlrbd.github.io/BPF/

Background: The rising feed costs and the need for sustainable alternatives have prompted the exploration of unconventional feed resources in poultry nutrition. Aim: This study aimed to evaluate the effects of incorporating cassava root meal (CRM) + leaf meal (LM) on the growth performance, carcass characteristics, hemo-biochemical parameters, and meat quality of broiler chickens. Methods: A total of 400 one-day-old Arbor Acres broiler chicks were randomly assigned to four dietary treatments: control (T-1, 0% CRM + LM), T-2 (5% CRM + 5% LM), T-3 (10% CRM + 10% LM), and T-4 (15% CRM + 15% LM). Each treatment group consisted of five replicates with 20 birds each, and the experiment lasted 35 days. Results: Broilers fed the T-2 diet demonstrated significantly (p < 0.001) improved body weight, feed intake, and feed efficiency ratio while exhibiting a better feed conversion ratio compared to other groups. Additionally, T-4 resulted in superior carcass characteristics. Although the proximate composition of thigh meat showed significant (p < 0.001) variations, but parameters such as crude protein, ash, and ether extract remained unaffected in breast meat. Diet T-2 also had the highest levels of total phenolic content, total flavonoid content, and antioxidant activity (DPPH scavenging), alongside excellent sensory acceptability. Conclusion: Overall, these findings indicate that incorporating 5% CRM + 5% LM (T-2) in broiler diets optimizes growth performance, meat quality, and health without adverse effects. This study highlights the potential of CRM and LM as a sustainable and cost-effective feed ingredient for broiler production, particularly in Asia, where feed costs pose significant challenges.

Introduction: Diabetes mellitus (DM) is a prevalent metabolic disorder frequently leading to serious renal complications, particularly diabetic nephropathy. This retrospective case–control study investigated the levels and associations of commonly used enzymatic (serum creatinine and urea) and physiological (glomerular filtration rate [GFR]) markers of kidney function in diabetic patients compared to non-diabetic controls. Methodology: A total of 237 participants were enrolled, comprising 81 diabetic cases and 156 non-diabetic controls. Creatinine and urea levels were determined using enzymatic methods, measuring optical density, whereas GFR was calculated using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation, based on creatinine, age, and sex. Statistical comparisons include p-value, Pearson correlation, etc. Results: The diabetic group exhibited significantly higher mean levels of serum creatinine (2.08 ± 2.26 mg/dL) and urea (57.71 ± 38.75 mg/dL) and a significantly lower mean GFR (59.59 ± 34.16 mL/min/1.73 m2) compared to the non-diabetic control group (0.95 ± 0.69 mg/dL, 31.79 ± 20.49 mg/dL, and 96.72 ± 23.77 mL/min/1.73 m2, respectively; all comparisons with p < 0.005). Correlation analysis revealed a more scattered positive association between creatinine and urea, and a pronounced inverse correlation between GFR and both creatinine and urea in the diabetic cases, suggesting a compromised renal function profile. Conclusions: Our findings demonstrate a significant association between diabetes and impaired renal function, as evidenced by elevated creatinine and urea levels and reduced GFR. These readily available biomarkers are crucial prognostic indicators for the early detection and effective management of diabetic nephropathy, emphasizing the importance of rigorous metabolic and blood pressure control to mitigate disease progression.

This study investigates the geometrical, electronic, and optical properties of novel T-AlN monolayer using density functional theory calculations. The T-AlN nanosheet is confirmed to be a stable semiconductor, as evidenced by its negative cohesive energy, phonon frequencies, and a calculated bandgap of 2.897 eV. The interaction of toxic gases, CO, CO2, NO, NO2, and SO2, with both pristine T-AlN and P-doped T-AlN (T-AlN (P_N)) nanosheets was systematically analyzed to evaluate their adsorption behavior. The results reveal favorable gas–surface interactions, with adsorption energies ranging from − 0.006 eV to − 2.674 eV. Both T-AlN and P-doped T-AlN nanosheets exhibit peak sensitivities of 2.16 × 1024 and 5.69 × 1021, respectively, toward NO and NO2 gases at 300 K. The adsorption mechanism is energetically favorable, as evidenced by negative adsorption energy values, signifying an exothermic and thermodynamically stable process that promotes spontaneous interaction between the gas molecules and the nanosheet surfaces. Work function analysis indicates the highest values upon NO2 adsorption and the lowest for CO. Despite these changes, the associated deformation energies remain low (10⁻4 to 10⁻2 eV), suggesting that the structural integrity of the sheets is largely preserved. These findings highlight the potential of T-AlN and P-doped T-AlN nanosheets as effective candidates for toxic gas sensing applications.)

The genome-wide analysis identified 55 PeSTs (Passiflora edulis sugar transporters), having significant variations in exon–intron structure, protein motifs, cis-regulatory elements, and syntenic relationships, which might reveal their functional diversity. Phylogenetic analysis classified these genes into eight subfamilies, where the STP subfamily showed significant expansion during the process of evolution. In molecular docking, the strongest binding affinities in Glu–PePLT4, Fru–PeSTP10, Gal–PePLT4, and Suc–PeTMT2 complexes might reveal their substrate specificity and transport kinetics. Following that, the molecular dynamics simulation supported the stability of the docked complexes. The presence of significant light, hormone, and stress regulatory cis-elements among the PeST promoters might reveal their hormone and stress regulatory functions. The highest homologous pairs (62) of PeSTs with M. domestica during synteny analysis among five plant genomes might guide their duplication pattern across the genomes. RNA-seq-based expression analysis, following real-time qRT-PCR mediated validation of upregulated expression of PeERD6L-1, PeSTP6, PeSTP8, PePLT1, and PeTMT5 genes under drought, salt, cold, and heat stresses, might guide their potential regulatory roles in tolerance to the respective stresses. Significant protein–protein and protein-TFs interactions in PeSTs might reveal their inter-regulatory roles in transporting sugars. These critical findings might guide the plant biologists in developing a synthetic biology-guided circuit enabled multiple abiotic stress-tolerant high-sugar passion fruit.