A 28-year-old woman with facial asymmetry after aligner treatment visited our hospital. She complained of an asymmetric gummy smile and a deviated mental area developed after clear aligner treatment. On CT examination, occlusal cant was found, leading to facial asymmetry. We made a clinical diagnosis of jaw deformity with an asymmetric face, and recommended her orthognathic surgery using wire orthodontics. She accepted jaw surgery; however, she refused wire orthodontic treatment. Therefore, we selected bimaxillary osteotomy with a surgical-first approach using her clear aligner to correct the inclined occlusal plane and improve the deviated jaw. The functional occlusion could be established, and improvement of facial form could be gained with a proper occlusal plane. This case report is a rare case, in which retreatment of the surgical approach for bimaxillary osteotomy for marked facial asymmetry developed after aligner treatment. We must be aware of the necessity of thorough and careful examination to avoid misdiagnosis.

This study is an empirical assessment of the Capital Asset Pricing Model (CAPM), the BlackScholes option pricing model (Black-Scholes), and the PutCall Parity principle (PCP)in China's A-share equity market and the U.S. derivatives market. Using data from 2020 to 2023, the research will investigate whether these classical models can reliably describe real-world market behaviors. Precisely, the low R obtained from CAPM analysis of Kweichow Moutai and the CSI 300 Index suggests that the model is not sufficient to explain market dynamics. In the meantime, beta coefficients in the standard CAPM are negative and statistically insignificant, indicating the failure of single-factor risk measures to capture the market dynamics properly. For derivatives, testing of European options on AMZN and SPY shows that the BlackScholes model does have directionally consistent pricing. However, systematic deviations and volatility smiles indicate that, in a real market, there are persistent and unavoidable violations of constant volatility assumptions. Also, the putcall parity principle, although generally held, has small but persistent deviations caused by transaction costs, liquidity constraints, and other market frictions. All in all, findings show that the empirical accuracy of CAPM, BlackScholes and Put-Call Parity is limited by market structure, behavioral factors, and unrealistic assumptions. This study further demonstrates the need for multifactor modeling approaches that could enhance the validity of asset pricing models.

94 - Esthetic attractiveness of asymmetric smiles with ectopic maxillary canines: Orthodontist, laypeople and patient perspectives

In this paper, we apply the generalized double reduction theory to a nonlinear extension of the Black-Scholes equation, which is a foundational model in financial mathematics for pricing European options. The Lie symmetry method is used to identify point symmetries of the nonlinear PDE, and conservation laws are derived using the multiplier approach. We demonstrate how the symmetry reductions lead to simplified invariant solutions and discuss their implications for understanding nonlinear market behaviors. Numerical simulations are used to illustrate how nonlinearity modifies traditional option pricing surfaces. Finally, we discuss potential real-world applications such as volatility smiles, hedging strategies, and robustness of risk metrics.

The study aimed to describe the interdisciplinary non-surgical management of a severe skeletal Class II division 1 malocclusion with bimaxillary protrusion and asymmetric gummy smile using three-dimensional (3D) digital planning, skeletal anchorage, and unilateral botulinum toxin injection. A 38-year-old female presented with lip incompetence, a 4 mm unilateral gummy smile on the right side, and protrusive upper and lower incisors. Cephalometric analysis showed A point, nasion, B point (ANB) 4.1°, U1-SN 125°, and incisor mandibular plane angle (IMPA) 105°. The treatment plan included the extraction of teeth 24, 35, and 45; full fixed appliance therapy; two maxillary inter-radicular miniscrews and two mandibular buccal shelf miniscrews for en masse anterior retraction and vertical control; and unilateral botulinum toxin injection at the Yonsei point after debonding to reduce hyperactivity of the right upper lip elevator complex. Total treatment time was 24 months. Post-treatment records demonstrated improved facial profile, symmetrical smile, and Class I canine and molar relationships. Cephalometric changes included a reduction of ANB from 4.1° to 2.8°, U1-SN from 125° to 108.9°, and IMPA from 105° to 95.2°. Gingival display on the right side was reduced from 4 mm to within normal limits, with balanced smile esthetics. The combination of digital 3D planning, skeletal anchorage mechanics, and targeted unilateral botulinum toxin injection can effectively address both the dental-skeletal and soft-tissue components of an asymmetric gummy smile in a severe skeletal Class II case. This approach offers a predictable, minimally invasive alternative to orthognathic surgery for selected adult patients.

Affine Diffusion (AD) dynamics are frequently used for Valuation Adjustments ( xVA ) calculations due to their analytic tractability. However, these models cannot capture the market-implied skew and smile, which are relevant when computing xVA metrics. Hence, additional degrees of freedom are required to capture these market features. In this paper, we address this through an SDE with state-dependent coefficients. The SDE is consistent with the convex combination of a finite number of different AD dynamics. We combine Hull-White one-factor models where one model parameter is varied. We use the Randomized AD (RAnD) technique to parameterize the combination of dynamics. We refer to our SDE with state-dependent coefficients and the RAnD parametrization of the original models as the rHW model. The rHW model allows for efficient semi-analytic calibration to European swaptions through the analytic tractability of the Hull-White dynamics. We use a regression-based Monte-Carlo simulation to calculate exposures. In this setting, we demonstrate the significant effect of skew and smile on (potential future) exposures and xVA s of linear and early-exercise interest rate derivatives.

Abstract Using industry restatement contagion as an external negative shock, we study the effectiveness of enterprise risk management (ERM) in mitigating downside risk and enhancing investor confidence. We find that ERM curbs overinvestment and earnings misstatement among firms when other firms in their industry engage in undisclosed misstatements that are subsequently restated. Following the announcements of these industry restatements, peers with ERM experience a smaller increase in implied volatility skewness. These effects are driven by peers with young CEOs, complex segment structures, low prior earnings performance, and in competitive industries. Overall, our findings highlight ERM's role in bolstering investor confidence by effectively managing firms' underlying risks.

Abstract BackgroundPheochromocytoma is a rare catecholamine‐secreting tumor that often presents with symptoms such as hypertension, palpitations, and sweating due to excessive hormone production. In some cases, the catecholamine‐induced vasoconstriction and hypercoagulability associated with pheochromocytomas can lead to cerebrovascular accidents and venous thrombosis. We report a rare case of pheochromocytoma in a middle‐aged man who initially presented with a stroke and later developed a pulmonary embolism.Case PresentationA 44‐year‐old gentleman presented with sudden right‐sided weakness, numbness, and slurred speech, lasting for 6 h. His medical history included hypertension, for which he was on bisoprolol. On examination, he exhibited right‐sided facial weakness, asymmetric smile, and motor weakness (0/5 on the right). Brain computed tomography angiography revealed an infarction in the left middle cerebral artery territory, complicated by hemorrhagic transformation. Seven days later, he developed severe left‐sided abdominal and chest pain, sweating, and left upper quadrant tenderness. His labs showed leukocytosis, and chest radiography raised suspicion of pulmonary embolism (PE). A computed tomography (CT) pulmonary angiogram confirmed thrombi in the left lower lobe with moderate left pleural effusion. Abdominal ultrasound revealed a non‐vascular mass near the left kidney, which was later identified as a 3.6 cm × 4.3 cm adrenal mass on CT. Biochemical tests confirmed pheochromocytoma. An FDG‐PET scan suggested an intense FDG‐avid left adrenal mass.ConclusionThis case demonstrates the rare association between pheochromocytoma and thrombotic events. Atypical presentations can complicate diagnosis, highlighting the need for early testing. Surgery remains the primary treatment, with long‐term follow‐up due to the risk of recurrence.

ABSTRACT Using a text‐based measure of peer opinions constructed from cryptocurrency‐related social media posts, we find that peer opinions contain valuable information about the prices of cryptocurrency options. Bitcoin options exhibit a volatility smile, which becomes steeper when peer opinions become bearish. The risk‐neutral skewness of Bitcoin returns implied by options prices becomes more negative in times of bearish opinions. The predictability of peer opinions for Bitcoin option prices remains robust after controlling for momentum, volatility, demand pressures, news effects, and other sentiment measures, and exhibits no evidence of reversal over time. This effect is pronounced when Bitcoin attracts high investor attention, more diverse opinions about Bitcoin are expressed on social media, and Bitcoin options are more actively traded. We find similar results for Ethereum options.

This case report describes the interdisciplinary management of a 58-year-old female patient with a misaligned dental implant in the left maxillary lateral incisor region, causing aesthetic and functional challenges. Initial assessments revealed significant bone loss around the compromised implant, an asymmetric smile, and excessive gingival display. The treatment included slow orthodontic extrusion to reposition adjacent teeth, promoting bone and periodontal regeneration, and orthodontic intrusion on the contralateral side to correct occlusal cant, and improve gingival aesthetics. Aligners with mini-screw anchorage ensured precise tooth movement and improved conditions for soft tissue grafting. Periodontal procedures enhanced tissue architecture and supported long-term stability, while the final prosthetic rehabilitation successfully restored function and aesthetics, emphasizing the importance of interdisciplinary collaboration for complex cases.

A self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p, q)-Hawkes model, has recently been introduced. The model generalises the Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p, q) model where the associated state process is driven by the counting process itself. The proposed model preserves the same degree of tractability as the Hawkes process, but it can reproduce more complex time-dependent structures observed in several market data. The paper presents a new model of asset price dynamics based on the CARMA(p, q)-Hawkes model. It is constructed using a compound version of it with a random jump size that is independent of both the counting and the intensity processes and can be employed as the main block for pure jump and (stochastic volatility) jump-diffusion processes. The numerical results for pricing European options illustrate that the new model can replicate the volatility smile observed in financial markets. Through an empirical analysis, which is presented as a calibration exercise, we highlight the role of higher order autoregressive and moving average parameters in pricing options.

Abstract Chiral N‐sulfinyl amides have recently emerged as powerful reagents for asymmetric, radical‐mediated Smiles rearrangements, imparting excellent levels of relative and absolute stereocontrol in the intra‐ and intermolecular translocation of aryl groups. Here, we capitalize on the much more readily available and abundant chiral sulfoxides, which, in combination with radical precursors and alkylating reagents, afford enantioenriched sulfur‐containing molecules via a photocatalytic multicomponent asymmetric sulfinyl‐Smiles rearrangement with retention of “SO”. This cascade process involves radical addition, a stereocontrolled 1,5‐aryl migration, and subsequent C─S bond formation, forging two new C─C bonds and a C─S bond in a single step under mild conditions. The resulting enantioenriched sulfur‐containing scaffolds are not only common in pharmaceuticals and bioactive compounds but also serve as versatile synthetic intermediates, as demonstrated by their efficient derivatization into diverse motifs.

Chiral N‐sulfinyl amides have recently emerged as powerful reagents for asymmetric, radical‐mediated Smiles rearrangements, imparting excellent levels of relative and absolute stereocontrol in the intra‐ and intermolecular translocation of aryl groups. Here, we capitalize on the much more readily available and abundant chiral sulfoxides, which, in combination with radical precursors and alkylating reagents, afford enantioenriched sulfur‐containing molecules via a photocatalytic multicomponent asymmetric sulfinyl‐Smiles rearrangement with retention of “SO”. This cascade process involves radical addition, a stereocontrolled 1,5‐aryl migration, and subsequent C─S bond formation, forging two new C─C bonds and a C─S bond in a single step under mild conditions. The resulting enantioenriched sulfur‐containing scaffolds are not only common in pharmaceuticals and bioactive compounds but also serve as versatile synthetic intermediates, as demonstrated by their efficient derivatization into diverse motifs.

A 34-year-old Korean man presented with an asymmetric smile, characterized by reduced activity in the left lip elevator muscles, including the levator labii superioris, levator labii superioris alaeque nasi, zygomaticus minor, and risorius. An electrical muscle stimulation device was employed to target these muscles in 20-minute sessions. Immediate improvements in symmetry were noted after each session. The treatment regimen consisted of 10 sessions over 10 weeks, with the results persisting for at least 3 months. The patient reported high satisfaction with the esthetic and functional outcomes.

This work provides an improved Black-Scholes model by incorporating inflation rate, dividend yield and risk free rate. The resulting pricing equation for derivatives and, in particular, the formula for European call options is then shown to depend explicitly on the drift of the underlying asset, which is following a geometric Brownian motion. It is visualized that with the present model, the predicted results by the model could be closer to real data. The adjusted pricing model could partly also explain the mystery of volatility smile. The present model also provides answers to many finance professionals and academics who have been intrigued by the effect of inflation rate, dividend yield and risk free of their asset. The model provides generally different fair values for financial derivatives compared to the Black-Scholes model. In particular, the present model predicts that the original Black-Scholes model tends to undervalue for example European call options.

Despite its synthetic potential, catalytic enantioselective Smiles rearrangement has remained elusive. Through the directed evolution of P450 radical aryl migratases (P450Smiles's), we describe the first example of catalytic enantioselective Smiles rearrangement. A range of racemic N-arylsulfonyl-α-chloroamides could be transformed by P450Smiles in an enantioconvergent manner, affording acyclic amide products possessing an all-carbon quaternary stereocenter with excellent chemo- and enantioselectivity. Both electron-rich and electron-deficient substituents were compatible with the migrating aryl group, demonstrating this P450-catalyzed Smiles rearrangement is insensitive to the electronic properties of the migrating group. Importantly, our evolved P450 variants were capable of overriding the innate cyclization activity of the N-alkyl amidyl radical intermediate, allowing the chemoselective reductive formation of acyclic products. Classical molecular dynamics (MD) simulations revealed this unusual enzyme-controlled chemoselectivity stems from the restricted conformation of the amidyl radical within the enzyme active site, disfavoring the cyclization pathway. This new-to-nature biocatalytic asymmetric Smiles rearrangement showcases the synthetic potential of enzymatic chemo- and enantioselectivity control over highly reactive radical intermediates eluding small-molecule catalysts.

ABSTRACTSince the inception of Volatility Index (VIX) options trading, academic literature has persistently sought accurate methods for jointly calibrating the prices of the S&P 500 index (SPX) and VIX options. This study introduces a novel nonparametric approach, called the joint implied willow tree (JIWT) method, aimed at resolving this joint calibration challenge. The resulting willow tree adheres to the martingale constraint for the SPX and ensures that the VIX is derived as the implied volatility of a 30‐day log contract on the SPX. A notable advantage of our method is its ability to recover not only the unconditional probabilities for a fixed maturity but also the conditional probabilities across different maturities. Consequently, we reconstruct the entire term structure of the SPX, aligning it with market information from both SPX and VIX options. Numerical and empirical analyses demonstrate that the JIWT method excels in accurately capturing the volatility smile of SPX and VIX across various maturities.

ABSTRACT Aim To evaluate the reliability of a free motion analysis method in the evaluation of the 2D dynamic asymmetry of smiles using smartphone technology. Materials and methods Twenty-six healthy adult females were included in this study. Four facial bilateral landmarks were marked on participants’ mouths and noses. A smartphone camera was used to record a video of the maximum smile of each participant. Each video was imported into a free motion analysis software program separately, that was used to track the landmarks’ speeds and distances during smiling. The asymmetry scores of the landmark motions were calculated by measuring the absolute differences between the right and left sides, and in perfectly symmetrical smiles the asymmetry scores would be zero. After an interval of a month, the asymmetry scores were re-calculated. The means of the absolute differences in the repeated distances and speeds for all the landmarks were calculated. Results The total errors of the repeated distances and speeds were around 0.4 millimetres (mm), except for asymmetrical maximum smile speeds, the errors were around 0.7 mm/sec. Intra-class correlation test showed high correlations between repeated asymmetry scores after a one-month interval. The asymmetry scores of the distances of landmarks’ motions at mid-smile were less than at maximum smile, although the peak asymmetry of speed occurred at the mid-smile frames rather than the maximum smile frames. Conclusions Motion analysis method is a reliable technique for analysis of 2D dynamic asymmetry of facial smiles, with acceptable accuracy. Using smartphone technology is clinically convenient and affordable.

PurposeSurgical resection of oral cancers requires meticulous planning to achieve clear margins and minimize potential morbidity. This study aimed to compare postoperative surgical and functional outcomes following central and lateral lip-split approaches used for resection and reconstruction of oral tumours.MethodsA retrospective review of 79 cases involving lip-split procedures for head and neck cancers was conducted. Data were collected from a prospectively recorded database (December 2015 to December 2022). Statistical analyses compared patient demographics, intraoperative characteristics, and postoperative outcomes between central and lateral lip-split cohorts.ResultsLateral lip splits were associated with higher rates of postoperative complications (p = 0.008), including return to theatre (p = 0.015), and functional issues including asymmetric smile (p = 0.009). No significant differences were observed in readmission rates, length of stay, or time to oral diet commencement (p > 0.05).ConclusionsLip-split procedures remain valuable for resection and reconstruction of oral and oropharyngeal tumours. Lateral lip splits are associated with poorer outcomes when compared to central approaches. Appropriate selection of lip splitting approaches should consider tumour location, resection margins, patient comorbidities and preferences, and surgical preferences.

In 1973, Fischer Black and Myron Scholes unveiled the Black-Scholes option pricing model, a groundbreaking contribution that profoundly influenced the domain of option pricing theory. The introduction of the Black-Scholes pricing formula has garnered substantial acclaim across both academic and industrial spheres, leading to its widespread dissemination and application. This formula not only underscores its vital significance but also exemplifies its unique position as a cornerstone of financial theory, reshaping how options are valued and traded in markets worldwide. However, in the real financial market, the Black-Scholes option pricing model has a serious deviation from empirical research in option pricing, which reduces its practicality and accuracy. This paper first briefly introduces the basic knowledge of options, covering both option-related concepts and option pricing theories, gives the definition of Black-Scholes option pricing deviation, and explains the volatility smile theory in detail. Starting from the probability of positive returns and the beliefs of traders, the probability of call option returns is obtained from historical trading data, and then decisions are made from these probabilities to overcome the deviations caused by Black-Scholes European option pricing and find an option pricing model that is more consistent with the market price of options. Through comprehensive simulation studies utilizing synthesized data, we conduct rigorous empirical tests to compare this theoretical model with the Black-Scholes option pricing model. The market prices of call options are derived from investor sentiments, allowing us to validate all three types of deviations from the Black-Scholes pricing formula within this numerical framework. The results reveal that the growth rates of stock returns can effectively serve as a substitute for the volatility smile, thereby facilitating their exclusion from risk-neutral analyses. These insights significantly enhance our understanding of option pricing dynamics in real-world scenarios.