In this paper, we study a multi-agent scheduling problem for organising the operations within the operating room department. The head of the surgeon group and individual surgeons are together responsible for the surgeon schedule and surgical case planning. The surgeon head allocates time blocks to individual surgeons, whereas individual surgeons determine the planning of surgical cases independently, which might degrade the schedule quality envisaged by the surgeon head. The bilevel optimisation under study seeks an optimal Nash equilibrium solution -- a surgeon schedule and surgical case plan that optimise the objectives of the surgeon head, while ensuring that no individual surgeon can improve their own objective within the allocated time blocks. We propose a dedicated branch-and-price that adds lazy constraints to the formulation of surgeon-specific pricing problems to ensure an optimal bilevel feasible solution is retrieved. In this way, the surgeon head respects the objective requirements of the individual surgeons and the solution space can be searched efficiently. In the computational experiments, we validate the performance of the proposed algorithm and its dedicated compon
In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options [1]. At the money (X= K) for American options, the expected payoff of both the call and put options is zero. Shepp investigated several stochastic optimization problems using martingale and stopping time theories [2,5,6]. One of the problems he investigated was how to optimize the stock price using both the Black-Scholes (multiplicative) and the Bachelier (additive) models [7,6] for the American option above the strike price K (exercise price) to a stopping point. In order to explore the non-relativistic quantum effect on the expected payoff for both the call and put options at the money, we assumed the stock price to undergo a stochastic process governed by the Bachelier (additive) model [4]. Further, using Ito calculus and martingale theory, we obtained a differential equation for the expected payoff for both the call and put options in terms of delta and gamma. We also obtained the solution to the non-relativistic Schroedinger equation as the ex
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniqueness of the solution to the difference equation corresponding to the variational inequality for pricing the perpetual American option and the solution representation are provided and the fact that the solution to the difference equation converges to the viscosity solution to the variational inequality is proved. It is shown that the limits of the prices of variational inequality and BTM models for American Option when the maturity goes to infinity do not depend on time and they become the prices of the perpetual American option.
For an autonomous robotic system, monitoring surgeon actions and assisting the main surgeon during a procedure can be very challenging. The challenges come from the peculiar structure of the surgical scene, the greater similarity in appearance of actions performed via tools in a cavity compared to, say, human actions in unconstrained environments, as well as from the motion of the endoscopic camera. This paper presents ESAD, the first large-scale dataset designed to tackle the problem of surgeon action detection in endoscopic minimally invasive surgery. ESAD aims at contributing to increase the effectiveness and reliability of surgical assistant robots by realistically testing their awareness of the actions performed by a surgeon. The dataset provides bounding box annotation for 21 action classes on real endoscopic video frames captured during prostatectomy, and was used as the basis of a recent MIDL 2020 challenge. We also present an analysis of the dataset conducted using the baseline model which was released as part of the challenge, and a description of the top performing models submitted to the challenge together with the results they obtained. This study provides significant
We study the obstacle problem associated with the American chooser option. The obstacle is given by the maximum of an American call option and an American put option, which, in turn, can be expressed as the maximum of the solutions to the corresponding obstacle problems. This structure makes the obstacle problem particularly challenging and non-trivial. Using theoretical analysis, we overcome these difficulties and establish the existence and uniqueness of a strong solution. Furthermore, we rigorously prove the monotonicity and smoothness of the free boundary arising from the obstacle problem.
Representations of AI agents in user interfaces and robotics are predominantly White, not only in terms of facial and skin features, but also in the synthetic voices they use. In this paper we explore some unexpected challenges in the representation of race we found in the process of developing an U.S. English Text-to-Speech (TTS) system aimed to sound like an educated, professional, regional accent-free African American woman. The paper starts by presenting the results of focus groups with African American IT professionals where guidelines and challenges for the creation of a representative and appropriate TTS system were discussed and gathered, followed by a discussion about some of the technical difficulties faced by the TTS system developers. We then describe two studies with U.S. English speakers where the participants were not able to attribute the correct race to the African American TTS voice while overwhelmingly correctly recognizing the race of a White TTS system of similar quality. A focus group with African American IT workers not only confirmed the representativeness of the African American voice we built, but also suggested that the surprising recognition results may
We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (FTAP). Using the FTAP, we get the dualities for the hedging prices of European and American options. Based on the hedging dualities, we also get the duality for the utility maximization. In the second part of the paper, we consider the market which admits non-dominated model uncertainty. We first establish the hedging result, and then using the hedging duality we further get the FTAP. Due to the technical difficulty stemming from the non-dominancy of the probability measure set, we use a discretization technique and apply the minimax theorem.
Robot-assisted surgical systems have demonstrated significant potential in enhancing surgical precision and minimizing human errors. However, existing systems cannot accommodate individual surgeons' unique preferences and requirements. Additionally, they primarily focus on general surgeries (e.g., laparoscopy) and are unsuitable for highly precise microsurgeries, such as ophthalmic procedures. Thus, we propose an image-guided approach for surgeon-centered autonomous agents that can adapt to the individual surgeon's skill level and preferred surgical techniques during ophthalmic cataract surgery. Our approach trains reinforcement and imitation learning agents simultaneously using curriculum learning approaches guided by image data to perform all tasks of the incision phase of cataract surgery. By integrating the surgeon's actions and preferences into the training process, our approach enables the robot to implicitly learn and adapt to the individual surgeon's unique techniques through surgeon-in-the-loop demonstrations. This results in a more intuitive and personalized surgical experience for the surgeon while ensuring consistent performance for the autonomous robotic apprentice. We
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partition of time interval with equal parts is used. A time interval partition method that allows binomial tree dynamics of the underlying asset's price is provided. Conditions under which the prices of American option by BTM and EDS have the monotonic property on time variable are found. Using convergence of EDS for variational inequality model of American options to viscosity solution the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied.
The surgical intervention is crucial to patient healthcare, and many studies have developed advanced algorithms to provide understanding and decision-making assistance for surgeons. Despite great progress, these algorithms are developed for a single specific task and scenario, and in practice require the manual combination of different functions, thus limiting the applicability. Thus, an intelligent and versatile surgical assistant is expected to accurately understand the surgeon's intentions and accordingly conduct the specific tasks to support the surgical process. In this work, by leveraging advanced multimodal large language models (MLLMs), we propose a Versatile Surgery Assistant (VS-Assistant) that can accurately understand the surgeon's intention and complete a series of surgical understanding tasks, e.g., surgical scene analysis, surgical instrument detection, and segmentation on demand. Specifically, to achieve superior surgical multimodal understanding, we devise a mixture of projectors (MOP) module to align the surgical MLLM in VS-Assistant to balance the natural and surgical knowledge. Moreover, we devise a surgical Function-Calling Tuning strategy to enable the VS-Assi
COVID-19 has aided the spread of racism, as well as national insecurity, distrust of immigrants, and general xenophobia, both of which may be linked to the rise in anti-Asian hate crimes during the pandemic. Coronavirus Disease 2019(COVID19) is thought to have originated in late December 2019 in Wuhan, China, and quickly spread across the world during the spring months of 2020. Asian Americans recorded in increase in racially based hate crimes including physical abuse and intimidation as COVID-19 spread throughout the United States. This research study was conducted by high school students in the Bay Area to compare the intention and characteristics of hate crimes against Asian Americans to hate crimes against African Americans. According to studies of both victim-related and most offender-related variables, hate crimes against Asian Americans have been rapidly growing in the United States and vary from those against African Americans. This leads to an investigation into the racial disparity between Asian American offenders and those of other races. The nature and characteristics of hate crimes against Asian Americans are compared to those of hate crimes against African Americans i
In this paper we examine the detailed theory of the American football in flight, with spin and air resistance included. We find the theory has much in common with the theory of a gyroscope and also rocket trajectory with a misaligned thruster. Unfortunately most of the air resistance data, for rocketry and ballistics, is for speeds of Mach 1 or higher, where the air resistance increases dramatically. We shall approximate a realistic air resistance, at the slower speeds of football flight, with a drag force proportional to cross sectional area and either $v$ or $v^2$, depending on speed, where $v$ is velocity of the football. We begin with a discussion of the motion, giving as much detail as possible without the use of complex analytic calculations. We point out the previous errors made with moments of inertia and make the necessary corrections for more accurate results. We show that the shape of an American football closely resembles a parabola of revolution.
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper investigates such a Call Put duality for perpetual American options. It turns out that the perpetual American Put price is equal to the perpetual American Call price in a model where, in addition to the previous exchanges between the spot price and the strike and between the interest and dividend rates, the local volatility function is modified. We prove that equality of the dual volatility functions only holds in the standard Black-Scholes model with constant volatility. Thanks to these duality results, we design a theoretical calibration procedure of the local volatility function from the perpetual Call and Put prices for a fixed spot price $x_0$. The knowledge of the Put (resp. Call) prices for all strikes enables to recover the local volatility function on the interval $(0,x_0)$ (resp. $(x_0,+\infty)$).
Surgical instrument segmentation is crucial in surgical scene understanding, thereby facilitating surgical safety. Existing algorithms directly detected all instruments of pre-defined categories in the input image, lacking the capability to segment specific instruments according to the surgeon's intention. During different stages of surgery, surgeons exhibit varying preferences and focus toward different surgical instruments. Therefore, an instrument segmentation algorithm that adheres to the surgeon's intention can minimize distractions from irrelevant instruments and assist surgeons to a great extent. The recent Segment Anything Model (SAM) reveals the capability to segment objects following prompts, but the manual annotations for prompts are impractical during the surgery. To address these limitations in operating rooms, we propose an audio-driven surgical instrument segmentation framework, named ASI-Seg, to accurately segment the required surgical instruments by parsing the audio commands of surgeons. Specifically, we propose an intention-oriented multimodal fusion to interpret the segmentation intention from audio commands and retrieve relevant instrument details to facilitate
American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times. Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors.
Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positions of holding versus shorting such options. Here we provide a unified framework and generalize the fundamental theorem of asset pricing (FTAP) and hedging dualities in arXiv:1502.06681 (to appear in Annals of Applied Probability) to the case where the investor can also short American options. Following arXiv:1502.06681, we assume that the longed American options are divisible. As for the shorted American options, we show that the divisibility plays no role regarding arbitrage property and hedging prices. Then using the method of enlarging probability spaces proposed in arXiv:1604.05517, we convert the shorted American options to European options, and establish the FTAP and sub- and super-hedging dualities in the enlarged space both with and without model uncertainty.
There is great scientific and popular interest in understanding the genetic history of populations in the Americas. We wish to understand when different regions of the continent were inhabited, where settlers came from, and how current inhabitants relate genetically to earlier populations. Recent studies unraveled parts of the genetic history of the continent using genotyping arrays and uniparental markers. The 1000 Genomes Project provides a unique opportunity for improving our understanding of population genetic history by providing over a hundred sequenced low coverage genomes and exomes from Colombian (CLM), Mexican-American (MXL), and Puerto Rican (PUR) populations. Here, we explore the genomic contributions of African, European, and Native American ancestry to these populations. Estimated Native American ancestry is 48% in MXL, 25% in CLM, and 13% in PUR. Native American ancestry in PUR is most closely related to populations surrounding the Orinoco River basin, confirming the Southern America ancestry of the Taíno people of the Caribbean. We present new methods to estimate the allele frequencies in the Native American fraction of the populations, and model their distribution
We consider the problem of finding a model-free upper bound on the price of an American put given the prices of a family of European puts on the same underlying asset. Specifically we assume that the American put must be exercised at either $T_1$ or $T_2$ and that we know the prices of all vanilla European puts with these maturities. In this setting we find a model which is consistent with European put prices and an associated exercise time, for which the price of the American put is maximal. Moreover we derive a cheapest superhedge. The model associated with the highest price of the American put is constructed from the left-curtain martingale transport of Beiglböck and Juillet.
We price American options using kernel-based approximations of the Volterra Heston model. We choose these approximations because they allow simulation-based techniques for pricing. We prove the convergence of American option prices in the approximating sequence of models towards the prices in the Volterra Heston model. A crucial step in the proof is to exploit the affine structure of the model in order to establish explicit formulas and convergence results for the conditional Fourier-Laplace transform of the log price and an adjusted version of the forward variance. We illustrate with numerical examples our convergence result and the behavior of American option prices with respect to certain parameters of the model.
We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional probability density function for the jump times and marks given the filtration of the Brownian motion and decompose the global controller-stopper problem into controller-stopper problems with respect to the Brownian filtration, which are determined by a backward induction. We apply our decomposition method to indifference pricing of American options under multiple default risk. The backward induction leads to a system of reflected backward stochastic differential equations (RBSDEs). We show that there exists a solution to this RBSDE system and that the solution provides a characterization of the value function.