The Segment Anything Model (SAM) serves as a fundamental model for semantic segmentation and demonstrates remarkable generalization capabilities across a wide range of downstream scenarios. In this empirical study, we examine SAM's robustness and zero-shot generalizability in the field of robotic surgery. We comprehensively explore different scenarios, including prompted and unprompted situations, bounding box and points-based prompt approaches, as well as the ability to generalize under corruptions and perturbations at five severity levels. Additionally, we compare the performance of SAM with state-of-the-art supervised models. We conduct all the experiments with two well-known robotic instrument segmentation datasets from MICCAI EndoVis 2017 and 2018 challenges. Our extensive evaluation results reveal that although SAM shows remarkable zero-shot generalization ability with bounding box prompts, it struggles to segment the whole instrument with point-based prompts and unprompted settings. Furthermore, our qualitative figures demonstrate that the model either failed to predict certain parts of the instrument mask (e.g., jaws, wrist) or predicted parts of the instrument as wrong classes in the scenario of overlapping instruments within the same bounding box or with the point-based prompt. In fact, SAM struggles to identify instruments in complex surgical scenarios characterized by the presence of blood, reflection, blur, and shade. Additionally, SAM is insufficiently robust to maintain high performance when subjected to various forms of data corruption. We also attempt to fine-tune SAM using Low-rank Adaptation (LoRA) and propose SurgicalSAM, which shows the capability in class-wise mask prediction without prompt. Therefore, we can argue that, without further domain-specific fine-tuning, SAM is not ready for downstream surgical tasks.
Ising models of emergent geometry are well known to possess ground states with many of the desired features of a low dimensional, Ricci flat vacuum. Further, excitations of these ground states can be shown to replicate the quantum dynamics of a free particle in the continuum limit. It would be a significant next step in the development of emergent Ising models to link them to an underlying physical theory that has General Relativity as its continuum limit. In this work we investigate how the canonical formulation of General Relativity can be used to construct such a discrete Hamiltonian using recent results in discrete differential geometry. We are able to demonstrate that the Ising models of emergent geometry are closely related to the model we propose, which we term the Canonical Ising Model, and may be interpreted as an approximation of discretized canonical general relativity.
Gravity does not naturally fit well with canonical quantization. Affine quantization is an alternative procedure that is similar to canonical quantization but may offer a positive result when canonical quantization fails to offer a positive result. Two simple examples given initially illustrate the power of affine quantization. These examples clearly point toward an affine quantization procedure that vastly simplifies a successful quantization of general relativity.
Given a topological property $P$, we say that the space $X$ is $P$-generated if for any subset $A\subset X$ that is not open in $X$ there is a subspace $Y \subset X$ with property $P$ such that $A\cap Y$ is not open in $Y$. (Of course, in this definition we could replace "open" with "closed".) In this paper we prove the following two results: (1) Every Lindelöf-generated regular space $X$ satisfying $|X|=Δ(X)=ω_1$ is $ω_1$-resolvable. (2) Any (countable extent)-generated regular space $X$ satisfying $Δ(X)>ω$ is $ω$-resolvable. These are significant strengthenings of our earlier results from [JSSz] which can be obtained from (1) and (2) by simply omitting the "-generated" part. Moreover, the second result improves a recent result of Filatova and Osipov from [FO] which states that Lindelöf-generated regular spaces of uncountable dispersion character are 2-resolvable. [FO] Maria A. Filatova, Alexander V. Osipov On resolvability of Lindelöf generated spaces, arxiv:1712.00803. Siberian Electronic Mathematical Reports, Vol. 14, (2017) pp. 1444-1444. [JSSz] Juhász, István; Soukup, Lajos; Szentmiklóssy, Zoltán, Regular spaces of small extent are $ω$-resolvable. Fund. Math. 228 (2015), no. 1, 27-46.
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.
The general field, containing all the macroscopic fields in it, is divided into the mass component, the source of which is the mass four-current, and the charge component, the source of which is the charge four-current. The mass component includes the gravitational field, acceleration field, pressure field, dissipation field, strong interaction and weak interaction fields, other vector fields. The charge component of the general field represents the electromagnetic field. With the help of the principle of least action we derived the field equations, the equation of the matter's motion in the general field, the equation for the metric, the energy and momentum of the system of matter and its fields, and calibrated the cosmological constant. The general field components are related to the corresponding vacuum field components so that the vacuum field generates the general field at the macroscopic level.
We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and find the Lie algebra corresponding to the optimal system of the symmetries. The symmetries in the optimal system allow us to transform the boundary condition to ordinary differential equations. The various cases for which the resulting systems of equations can be solved are identified. For each of these cases the boundary condition is integrated and the gravitational potentials are found explicitly. A particular group invariant solution produces a class of models which contains Euclidean stars as a special case. Our generalized model satisfies a linear equation of state in general. We thus establish a group theoretic basis for our generalized model with an equation of state. By considering a particular example we show that the weak, dominant and strong energy conditions are satisfied.
The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This suggests that the question of existence or non-existence of solutions to the original equations is more subtle than could perhaps be expected.
We present a definite formulation of the Principle of General Covariance (GCP) as a Principle of General Relativity with physical content and thus susceptible of verification or contradiction. To that end it is useful to introduce a kind of coordinates, that we call quasi-Minkowskian coordinates (QMC), as an empirical extension of the Minkowskian coordinates employed by the inertial observers in flat space-time to general observers in the curved situations in presence of gravitation. The QMC are operationally defined by some of the operational protocols through which the inertial observers determine their Minkowskian coordinates and may be mathematically characterized in a neighbourhood of the world-line of the corresponding observer. It is taken care of the fact that the set of all the operational protocols which are equivalent to measure a quantity in flat space-time split into inequivalent subsets of operational prescriptions under the presence of a gravitational field or when the observer is not inertial. We deal with the Hole Argument by resorting to de idea of the QMC and show how it is the metric field that supplies the physical meaning of coordinates and individuates point-events in regions of space-time where no other fields exist. Because of that the GCP has also value as a guiding principle supporting Einstein's appreciation of its heuristic worth in his reply to Kretschmann in 1918.
We construct an asymptotic series for a general solution of the Einstein equations near a sudden singularity. The solution is quasi isotropic and contains nine independent arbitrary functions of the space coordinates as required by the structure of the initial value problem.
Einstein considered general covariance to characterize the novelty of his General Theory of Relativity (GTR), but Kretschmann thought it merely a formal feature that any theory could have. The claim that GTR is "already parametrized" suggests analyzing substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar "clock fields," much as Einstein construed general covariance as the lack of preferred coordinates. Physicists often install gauge symmetries artificially with additional fields, as in the transition from Proca's to Stueckelberg's electromagnetism. Some post-positivist philosophers, due to realist sympathies, are committed to judging Stueckelberg's electromagnetism distinct from and inferior to Proca's. By contrast, physicists identify them, the differences being gauge-dependent and hence unreal. It is often useful to install gauge freedom in theories with broken gauge symmetries (second-class constraints) using a modified Batalin-Fradkin-Tyutin (BFT) procedure. Massive GTR, for which parametrization and a Lagrangian BFT-like procedure appear to coincide, mimics GTR's general covariance apart from telltale clock fields. A generalized procedure for installing artificial gauge freedom subsumes parametrization and BFT, while being more Lagrangian-friendly than BFT, leaving any primary constraints unchanged and using a non-BFT boundary condition. Artificial gauge freedom licenses a generalized Kretschmann objection. However, features of paradigm cases of artificial gauge freedom might help to demonstrate a principled distinction between substantive and merely formal gauge symmetry.
The general relativistic version is developed for Robertson's discussion of the Poynting-Robertson effect that he based on special relativity and Newtonian gravity for point radiation sources like stars. The general relativistic model uses a test radiation field of photons in outward radial motion with zero angular momentum in the equatorial plane of the exterior Schwarzschild or Kerr spacetime.
In a series of recent writings, John Roemer (1982a, 1982b, 1985, 1988) has made a provocative claim: exploitation and class are merely second-order concepts within Marxian theory, because both phenomena derive directly from differential ownership of productive assets (DOPA); indeed, exploitation remains a consistent index of economic injustice only if a “property relations” conception of exploitation replaces the common “labor-value” view. In sum, property relations, not the labor exchange, the labor proces, labor values, or even capitalist accumlation should bethecentral concern of Marxian theory.
The properties of multimomentum maps on null hypersurfaces, and their relation with the constraint analysis of General Relativity, are described. Unlike the case of spacelike hypersurfaces, some constraints which are second class in the Hamiltonian formalism turn out to contribute to the multimomentum map.
We discuss various features of the dynamical system determined by the flow of null geodesic generators of Cauchy horizons. Several examples with non--trivial (``chaotic'', ``strange attractors'', etc.) global behaviour are constructed. Those examples are relevant to the ``chronology protection conjecture'', and they show that the occurrence of ``fountains'' is {\em not} a generic feature of Cauchy horizons.
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected to half a percent using the binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.