The prevalence of low-quality content on online platforms is often attributed to the absence of meaningful entry requirements. This motivates us to investigate whether implicit or explicit entry barriers, alongside appropriate reward mechanisms, can enhance content quality. We present the first game-theoretic analysis of two distinct types of entry barriers in online content platforms. The first, a structural barrier, emerges from the collective behaviour of incumbent content providers which disadvantages new entrants. We show that both rank-order and proportional-share reward mechanisms induce such a structural barrier at Nash equilibrium. The second, a strategic barrier, involves the platform proactively imposing entry fees to discourage participation from low-quality contributors. We consider a scheme in which the platform redirects some or all of the entry fees into the reward pool. We formally demonstrate that this approach can improve overall content quality. Our findings establish a theoretical foundation for designing reward mechanisms coupled with entry fees to promote higher-quality content and support healthier online ecosystems.
Online market platforms play an increasingly powerful role in the economy. An empirical phenomenon is that platforms, such as Amazon, Apple, and DoorDash, also enter their own marketplaces, imitating successful products developed by third-party sellers. We formulate a Stackelberg model, where the platform acts as the leader by committing to an entry policy: when will it enter and compete on a product? We study this model through a theoretical and computational framework. We begin with a single seller, and consider different kinds of policies for entry. We characterize the seller's optimal explore-exploit strategy via a Gittins-index policy, and give an algorithm to compute the platform's optimal entry policy. We then consider multiple sellers, to account for competition and information spillover. Here, the Gittins-index characterization fails, and we employ deep reinforcement learning to examine seller equilibrium behavior. Our findings highlight the incentives that drive platform entry and seller innovation, consistent with empirical evidence from markets such as Amazon and Google Play, with implications for regulatory efforts to preserve innovation and market diversity.
In virtual reality, it is challenging to achieve satisfactory text entry speed/accuracy, ergonomics, usability, and learnability. To address this issue, we developed ErgoGlide, a novel lightweight and compact wearable device that facilitates text entry tasks in virtual environments. The proposed ErgoGlide can be regarded as a small trackball that is wearable on a user's finger like a ring. By using ErgoGlide with a hive-like virtual keyboard, the user can rotate the ball for key selections, making text entry intuitive and accurate. We conducted three user studies to evaluate ErgoGlide and found that key confirmation techniques have significant effects on text entry speed and the hive-like keyboard design significantly reduced thumb movements. Furthermore, ErgoGlide can significantly improve typing accuracy, ergonomics, and usability over previous text entry methods. Experimental results also indicated that the typing speed of ErgoGlide can be notably improved after training.
Over the history of planetary exploration, atmospheric entry vehicles have been used to deliver probes and landers to Venus, Mars, Jupiter, and Titan. While the entry vehicles are tools for furthering scientific exploration, by delivering probes and landers which perform in-situ exploration, the entry vehicle and trajectory design in itself is of significant interest. Entering an atmosphere subjects the vehicle to deceleration and aerodynamic heating loads which the vehicle must withstand to deliver the probe or the lander inside the atmosphere. The conditions encountered depend on the destination, the atmosphere-relative entry speed, the vehicle type, ballistic coefficient, the vehicle geometry, and the entry-flight path angle. The driving constraints are the peak aerodynamic deceleration, peak heat rate, and the total heat load encountered during the critical phase of the entry. Jupiter presents the most extreme entry conditions, while Titan presents the most benign entry environment. This study presents a survey of the design trade space for atmospheric entry missions across the Solar System using carpet plots, along with benchmarks from historical missions, which can serve as a
We model a market for data where an incumbent and a challenger compete for data from a producer. The incumbent has access to an exclusive data producer, and it uses this exclusive access, together with economies of scope in the aggregation of the data, as a strategy against the potential entry by the challenger. We assess the incumbent incentives to either deter or accommodate the entry of the challenger. We show that the incumbent will accommodate when the exclusive access is costly and when the economies of scope are low, and it will blockade or deter otherwise. The results would justify an access regulation that incentivizes the entry of the challenger, e.g., by increasing production costs for the exclusive data.
Research on text entry in Virtual Reality (VR) has gained popularity but the efficient entry of accented characters, characters with diacritical marks, in VR remains underexplored. Entering accented characters is supported on most capacitive touch keyboards through a long press on a base character and a subsequent selection of the accented character. However, entering those characters on physical keyboards is still challenging, as they require a recall and an entry of respective numeric codes. To address this issue this paper investigates three techniques to support accented character entry on physical keyboards in VR. Specifically, we compare a context-aware numeric code technique that does not require users to recall a code, a key-press-only condition in which the accented characters are dynamically remapped to physical keys next to a base character, and a multimodal technique, in which eye gaze is used to select the accented version of a base character previously selected by key-press on the keyboard. The results from our user study (n=18) reveal that both the key-press-only and the multimodal technique outperform the baseline technique in terms of text entry speed.
The study of planetary atmospheres is critical to our understanding of the origin and evolution of the Solar System. The combined effect of various physical and chemical processes over billions of years have resulted in a variety of planetary atmospheres across the Solar System. This paper performs a comparative study of planetary atmospheres and their engineering implications for future entry and aerocapture missions. The thick Venusian atmosphere results in high deceleration and heating rates and presents a demanding environment for both atmospheric entry and aerocapture. The thin Martian atmosphere allows low aerodynamic heating, but itself is not enough to decelerate a lander to sufficiently low speeds for a soft landing. With their enormous gravity wells, Jupiter and Saturn entry result in very high entry speeds, deceleration, and heating making them the most demanding destinations for atmospheric entry and impractical for aerocapture. Titan is a unique destination, with its low gravity and greatly extended thick atmosphere enabling low deceleration and heating loads for entry and aerocapture. Uranus and Neptune also have large gravity wells, resulting in high entry speeds, hi
Firms are more likely to introduce products in markets where they anticipate stronger demand. They also possess information that is unobserved to researchers. This creates endogenous selection bias in the estimation of demand parameters. With differentiated products, the entry decision violates the monotonicity conditions required for standard selection-correction methods to yield consistent demand estimates. Existing studies address this issue either by imposing strong assumptions about firms' information on demand at the time of entry or by jointly estimating a full equilibrium model of demand, pricing, and entry. Both strategies make the estimation of demand heavily reliant on supply-side assumptions. We propose a new semiparametric estimation method that addresses these limitations. Our approach exploits the correlation across products in their market-entry decisions to identify entry probabilities conditional not only on observable characteristics but also on latent variables that capture unobserved interdependencies among firms' entry choices. We refer to these probabilities as latent propensity scores. We show that the selection bias term in the demand equation is a convolut
We analyze how an incumbent antibiotic monopolist responds to the threat of post-entry Bertrand competition by a vertically differentiated rival. In a two-period model where current production drives future resistance, Bertrand competition leads to a winner-take-all outcome. We find that strategic deterrence is optimal regardless of bacterial cross-resistance to prospective rival drugs. In contrast with post-entry Cournot competition, anticipated price competition provides the incumbent with a stronger strategic incentive for conservation.
We analyze a two-period, two-market chain-store game in which an incumbent's conduct in one market is only sometimes seen in the other. This partial observability generates reputational spillovers across markets. We characterize equilibrium behavior by prior reputation: at high priors the strategic incumbent fights a lone early entrant (and mixes when both arrive together); at low priors it mixes against a single entrant and accommodates coordinated entry. Greater observability increases early fighting yet, because any accommodation is more widely noticed, raises the incidence of later entry. The results are robust to noisy signals and endogenous information acquisition, and extend naturally to many markets.
In this article we develop the direct and inverse scattering theory of the Ablowitz-Kaup-Newell-Segur (AKNS) system $\bv_x=(ik\zS+\CQ(x))\bv$, where $\zS$ is a diagonal $n\times n$ matrix with diagonal entries $1$ and $-1$ and a single zero diagonal entry and $\CQ(x)$ is an $n\times n$ potential anticommuting with $\zS$ with entries in $L^1(\R)$. We derive the time evolution of the scattering data which, through the inverse scattering transform, lead to the solution of the initial-value problem for a system of long-wave-short-wave equations.
Since the beginning of robotic interplanetary exploration nearly six decades ago, successful atmospheric entry has been accomplished at Venus, Earth, Mars, Jupiter, and Titan. More entry probe missions are planned to Venus, Titan, and Uranus in the next decade. Atmospheric entry subjects the vehicle to rapid deceleration and aerothermal loads which the vehicle must be designed for, to deliver the robotic instruments inside the atmosphere. The design of planetary probes and their mission architecture is complex, and involves various engineering constraints such as peak deceleration, heating rate, heating load, and communications which must be satisfied within the budget and schedule of cost constrained mission opportunities. Engineering design data from previous entry probe missions serve as a valuable reference for designing future missions. The present study compiles an augmented version of the blue book entry probe dataset, performs a comparative analysis of the entry conditions, and provides engineering rules of thumb for design of future missions. Using the dataset, the present study proposes a new empirical correlation which aims to more accurately predict the thermal protecti
This paper develops a sequential convex programming approach for Mars entry trajectory planning by range discretization. To improve the accuracy of numerical integration, the range of entry trajectory is selected as the independent variable rather than time or energy. A dilation factor is employed to normalize the entry dynamics and integration interval of the performance index so that the difficult free-final-time programming problem can be converted to a fixed-final-range optimization problem. The bank angle rate with respect to the range is introduced as the new control input in order to decouple the control from the state and facilitate convexification of constraints on the bank angle and its rate. The nonlinear bank angle rate constraint is further relaxed into a linear one via inequality relaxation. Moreover, the nonconvex minimum-time performance index is convexified by regarding flight time as a state variable. Then, the Mars entry trajectory planning problem can be formulated into the framework of convex programming after linearization. By range discretization and successive convexification, the reformulated Mars entry trajectory planning problem is transcribed into a seri
Thermal protection systems are a critical component of planetary exploration, enabling probes to enter the atmosphere and perform in-situ measurements. The aero-thermal conditions encountered during entry are destination and vehicle dependent, ranging from relatively benign conditions at Mars and Titan, to extreme conditions at Venus and Jupiter. The thermal protection system is a single-point-of-failure for both entry probe and aerocapture missions, and hence must be qualified using ground tests to ensure mission success. The high density Carbon-Phenolic which was used in the Galileo and the Pioneer Venus missions is no longer available due to the lack of the manufacturing base for its raw materials. To address the need for Venus and outer planet missions, NASA has developed the Heatshield for Extreme Environment Entry Technology (HEEET). The present study uses the Aerocapture Mission Analysis Tool (AMAT) to perform a comparative study of the thermal protection system requirements for various planetary destinations and the applicability of HEEET for future entry and aerocapture missions. The heat rate and stagnation pressure for aerocapture is significantly less compared to probe
In this paper, closed-loop entry guidance in a randomly perturbed atmosphere, using bank angle control, is posed as a stochastic optimal control problem. The entry trajectory, as well as the closed-loop controls, are both modeled as random processes with statistics determined by the entry dynamics, the entry guidance, and the probabilistic structure of altitude-dependent atmospheric density variations. The entry guidance, which is parameterized as a sequence of linear feedback gains, is designed to steer the probability distribution of the entry trajectories while satisfying bounds on the allowable control inputs and on the maximum allowable state errors. Numerical simulations of a Mars entry scenario demonstrate improved range targeting performance with approximately 50% lower 1st and 99th percentile final range errors when using the developed stochastic guidance scheme as compared to the existing Apollo final phase algorithm.
This paper presents a new text entry technique, namely H4-Writer, designed for gaze controlled environments and aimed at reducing average KSPC . and spatial footprint. It also presents an empirical evaluation of this proposed system by using three different input devices: mouse, gamepad, and eye tracker. The experiment was conducted using 9 participants and the obtained data were used to compare the entry speeds, efficiency and KSPC of H4-Writer for all the devices. Over three blocks, the average entry speed was 3.54 wpm for the mouse, 3.33 wpm for the gamepad and only 2.11 wpm for the eye tracker. While the eye tracker fared poorly compared to the mouse and the gamepad on entry speed, it showed significant improvement in entry speed over progressing blocks indicating increase in entry speed with practice. A full longitudinal study was conducted to indicate this. The average KSPC of all the three devices over all the text phrases entered was 2.62, which is significantly lower compared to other hand writing recognizing text entry techniques like EdgeWrite. An analysis of the blocks revealed improvement in error rate, efficiency and KSPC values with progressing block numbers as the p
In this paper, we study Brownian-type operators, which are upper triangular $2\times 2$ block matrix operators with entries satisfying some algebraic constraints. We establish a lifting theorem stating that any Brownian-type operator with subnormal $(2,2)$ entry lifts to a Brownian-type operator with normal $(2,2)$ entry, where lifting is understood in the sense of extending entries of the block matrices representing the operators in question. The spectral inclusion and the filling in holes theorems are obtained for such operators.
Virus entry is a multistep process that triggers a variety of cellular pathways interconnecting into a complex network, yet the molecular complexity of this network remains largely unsolved. Here, by employing systems biology approach, we reveal a systemic virus-entry network initiated by human cytomegalovirus (HCMV), a widespread opportunistic pathogen. This network contains all known interactions and functional modules (i.e. groups of proteins) coordinately responding to HCMV entry. The number of both genes and functional modules activated in this network dramatically declines shortly, within 25 min post-infection. While modules annotated as receptor system, ion transport, and immune response are continuously activated during the entire process of HCMV entry, those for cell adhesion and skeletal movement are specifically activated during viral early attachment, and those for immune response during virus entry. HCMV entry requires a complex receptor network involving different cellular components, comprising not only cell surface receptors, but also pathway components in signal transduction, skeletal development, immune response, endocytosis, ion transport, macromolecule metabolis
The performance optimization for a combined ascent-entry mission subject to constraints on heating rate and heating load is studied. The ascent vehicle is modeled as a three-stage rocket that places the vehicle onto a suborbital exo-atmopheric trajectory after which the vehicle undergoes an unpowered entry and descent to a vertically downward terminal condition. The entry vehicle is modeled as a high lift-to-drag ratio vehicle that is capable of withstanding high levels of thermal and structural loads. A performance index is designed to improve control margin while attenuating phugoid oscillations during atmospheric entry. Furthermore, a mission corresponding to a prototype launch and target point is used in this study. The trajectory optimization problem is formulated as a multiple-phase optimal control problem, and the optimal control problem is solved using an adaptive Gaussian quadrature collocation method. A key aspect of the optimized trajectories is that, for particular ranges of maximum allowable heating rate and heating load during entry, relatively small adjustments made during ascent can potentially decrease the control effort required during atmospheric entry. Outside o
We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical. The model captures realistic features observed in many economic observables, which can be explained as market-driven firm entries/exits, worker inflow/outflow, and income growth/loss. This model is not conservative and, despite the asymmetry in the entry and exit rates, we find that the system eventually relaxes to a stationary distribution. Moreover, our analysis reveals three distinct dynamical regimes in the moments of the distribution, arising from the interplay between volatility, drift, entry, and exit rates. We further derive the survival probability and the mean first-passage time associated with the observed variable reaching certain threshold under the competing entry-exit processes. Interestingly, we identify an optimal exit rate that minimizes the mean first-passage time, providing insights into how entry and exit policies can influence the outcome of the system. These results should be useful for understanding the long-run behavior