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Michael

Publications and source records attributed to Michael.

At least 19 recordsLinked to original sources

Robust Cross-Domain Generalization Using Unlabeled Target Data with Source-Domain Supervision

It is often desirable to generalize medical imaging AI models trained with dense annotations to data acquired from different ultrasound scanners or clinical sites; however, retraining these models with new annotations is often difficult and costly. We examine this challenge in pediatric wrist fracture assessment using point-of-care ultrasound (POCUS), where fractures are common and can be effectively triaged via ultrasound. AI has shown radiologist-level performance for fracture detection, often aided by high-quality bony structure segmentation. However, due to significant domain shifts, models perform poorly on data from other centers or probes, and obtaining segmentation labels across devices is impractical due to manual annotation effort and data privacy concerns. To address this, we propose a target-informed self-supervised pretraining and model-ensemble strategy. Specifically, our approach combines masked image modeling (MIM) and contrastive learning to learn target-domain structural representations without labels, and introduces a confidence-aware infusion head to adaptively integrate predictions. The source dataset, collected with a Philips Lumify probe, contained dense labels, while the target dataset, acquired with a TeleMED portable probe, was unlabeled. The datasets were kept strictly separate throughout the entire process. Our method used labeled source data for supervised training and leveraged target-domain pretraining to improve generalization. On 318 images from 62 pediatric POCUS videos, this approach significantly improved cross-device performance, achieving over 6% Dice improvement on the target domain versus the baseline. These results demonstrate a label-efficient and privacy-preserving approach for cross-device-robust ultrasound AI, offering a framework that can be extended to multi-center studies or federated learning setups.

cs.CV

Real-Time Dynamic N-1 Screening: Identifying High-Risk Lines and Transformers After Common Faults

Power system operators routinely perform N-1 contingency analysis, yet conventional tools provide limited guidance on which lines or transformers deserve heightened attention during fast post-fault transients. In particular, static screening does not reveal whether (1) the same faulted line repeatedly triggers severe downstream overloads, or (2) a specific transformer emerges as vulnerable across many distinct fault scenarios. This paper introduces a real-time dynamic N-1 screening framework that addresses this gap by estimating, for each counterfactual single-phase transmission fault, the probability of transient overcurrent on critical grid elements. The output is an operator-facing dashboard that ranks (a) faulted lines whose outages most frequently lead to dangerous transformer overloads, and (b) transformers that consistently overload across top-risk scenarios, both of which are actionable indicators for real-time situational awareness. The approach models post-fault electromechanical dynamics using a linear stochastic formulation of the swing equations with short-lived, fault-localized uncertainty, and combines analytic transient evaluation with cross-entropy based importance sampling to efficiently estimate rare but high-impact events. All N-1 contingencies are evaluated in parallel with linear computational complexity. The framework is demonstrated on the IEEE 118-bus system, where it reveals latent high-risk lines and transformers that remain invisible under deterministic dynamic or static N-1 analysis. Results show orders-of-magnitude computational speedup relative to brute-force Monte Carlo, enabling practical deployment within real-time operational cycles.

math.OC

Real-Time Stochastic Assessment of Dynamic N-1 Grid Contingencies

Power system operators need tools for rapid, real-time counterfactual assessments of grid security under fast-changing conditions. Traditional N-1 contingency analysis lacks dynamic evaluation, especially of frequency swings from common faults. This paper introduces a real-time dashboard framework to screen dynamic contingencies. It assumes: (a) the grid starts in a balanced state; (b) faults can occur randomly on any transmission line, temporarily de-energizing and then reconnecting it within about one second; and (c) contingencies are flagged if post-fault transients cause line flows to exceed safety thresholds. The key contributions are: (1) Overload Indicator: a system-wide metric quantifying integrated N-1 dynamic risk from a given state; (2) Scalable Fault Evaluation Algorithm: a linear-scaling method to assess dynamic fault impacts without brute-force simulations; and (3) Risk Estimation: a Cross Entropy Adaptive Importance Sampling method estimating the likelihood of low probability by high risk events, e.g. associated with potential transformer over-current. We demonstrate the framework on the Israeli transmission power grid (IG).

math.DS

Perceptive Locomotion with Controllable Pace and Natural Gait Transitions Over Uneven Terrains

This work developed a learning framework for perceptive legged locomotion that combines visual feedback, proprioceptive information, and active gait regulation of foot-ground contacts. The perception requires only one forward-facing camera to obtain the heightmap, and the active regulation of gait paces and traveling velocity are realized through our formulation of CPG-based high-level imitation of foot-ground contacts. Through this framework, an end-user has the ability to command task-level inputs to control different walking speeds and gait frequencies according to the traversal of different terrains, which enables more reliable negotiation with encountered obstacles. The results demonstrated that the learned perceptive locomotion policy followed task-level control inputs with intended behaviors, and was robust in presence of unseen terrains and external force perturbations. A video demonstration can be found at https://youtu.be/OTzlWzDfAe8, and the codebase at https://github.com/jennyzzt/perceptual-locomotion.

cs.RO

Hereditary Interval Algebras and Cardinal Characteristics of the Continuum

An interval algebra is a Boolean algebra which is isomorphic to the algebra of finite unions of half-open intervals, of a linearly ordered set. An interval algebra is hereditary if every subalgebra is an interval algebra. We answer a question of M. Bekkali and S. Todor\v{c}evi\'c, by showing that it is consistent that every $\sigma$-centered interval algebra of size $\mathfrak{b}$ is hereditary. We also show that there is, in ZFC, an hereditary interval algebra of cardinality $\aleph_1.$

math.LO

A survey on Polynomial in momenta integrals for billiard problems

In this paper we give a short survey of recent results on algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the algebraic technique we study the existence of polynomial integrals for the two-sided magnetic billiards introduced by Kozlov and Polikarpov.

math.DS

In search of periodic solutions for a reduction of the Benney chain

We search for smooth periodic solutions for the system of quasi-linear PDEs known as the Lax dispersionless reduction of the Benney moments chain. It is naturally related to the existence of a polynomial in momenta integral for a Classical Hamiltonian system with 1,5 degrees of freedom. For the solution in question it is not known a-priori if the system is elliptic or hyperbolic or of mixed type. We consider two possible regimes for the solution. The first is the case of only one real eigenvalue, where we can completely classify the solutions. The second case of strict Hyperbolicity is really a challenge. We find a remarkable 2 by 2 reduction which is strictly Hyperbolic but violates the condition of genuine non-linearity.

math-ph

Integrable magnetic geodesic flows on 2-torus: new example via quasi-linear system of PDEs

The only one example has been known of magnetic geodesic flow on the 2-torus which has a polynomial in momenta integral independent of the Hamiltonian. In this example the integral is linear in momenta and corresponds to a one parametric group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on one energy level is considered. This problem can be reduced to a remarkable Semi-hamiltonian system of quasi-linear PDEs and to the question of existence of smooth periodic solutions for this system. Our main result states that the pair of Liouville metric with zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of a quadratic in momenta integral. Thus our construction gives a new example of smooth periodic solution to the Semi-hamiltonian (Rich) quasi-linear system of PDEs.

math.DS

Algebraic non-integrability of magnetic billiards

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece $\gamma$ of the boundary must be algebraic and either is a circle or satisfies very strong restrictions. In particular in the case of ellipse it follows that magnetic billiard is algebraically not integrable for all magnitudes of the magnetic field. We conjecture that circle is the only integrable magnetic billiard not only in the algebraic sense, but for a broader meaning of integrability. We also introduce the model of Outer magnetic billiards. As an application of our method we prove analogous results on algebraically integrable Outer magnetic billiards.

math.DG

Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane

We consider a convex curve $\gamma$ lying on the Sphere or Hyperbolic plane. We study the problem of existence of polynomial in velocities integrals for Birkhoff billiard inside the domain bounded by $\gamma$. We extend the result by S. Bolotin (1992) and get new obstructions on polynomial integrability in terms of the dual curve $\Gamma$. We follow a method which was introduced by S. Tabachnikov for Outer billiards in the plane and was applied later on in our recent paper to Birkhoff billiards with the help of a new the so called Angular billiard.

math.DG

On Newton equations which are totally integrable at infinity

In this paper Hamiltonian system of time dependent periodic Newton equations is studied. It is shown that for dimensions $3$ and higher the following rigidity results holds true: If all the orbits in a neighborhood of infinity are action minimizing then the potential must be constant. This gives a generalization of the previous result \cite{B3}, where it was required all the orbits to be minimal. As a result we have the following application: Suppose that for the time-1 map of the Hamiltonian flow there exists a neighborhood of infinity which is filled by invariant Lagrangian tori homologous to the zero section. Then the potential must be constant. Remarkably, the statement is false for $n=1$ case and remains unknown to the author for $n=2$.

math.DS

Effective bounds in E.Hopf rigidity for billiards and geodesic flows

In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e. if $\mathcal{M}$ occupies the whole phase space we recover the E.Hopf rigidity. We give these estimates in two cases: the first is the case of convex billiards in the plane, sphere or hyperbolic plane. The second is the case of conformally flat Riemannian metrics on a torus. It seems to be a challenging question to understand such a quantitative bounds for Burago-Ivanov theorem.

math.DS

Integrable geodesic flows on 2-torus: formal solutions and variational principle

In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic flow on 2-torus. We proved in [3] that this is a semi-Hamiltonian system and we show here that the metric associated with the system is a metric of Egorov type. We use this fact in order to prove that in the case of integrals of degree three and four the system is in fact equivalent to a single remarkable equation of order 3 and 4 respectively. Remarkably the equation for the case of degree four has variational meaning: it is Euler-Lagrange equation of a variational principle. Next we prove that this equation for $n=4$ has formal double periodic solutions as a series in a small parameter.

math.DG

A remark on the number of invisible directions for a smooth Riemannian metric

In this note we give a construction of a smooth Riemannian metric on R^n which is standard Euclidean outside a compact set K and such that it has N = n(n + 1)=2 invisible directions, meaning that all geodesics lines passing through the set K in these directions remain the same straight lines on exit. For example in the plane our construction gives three invisible directions. This is in contrast with billiard type obstacles where a very sophisticated example due to A.Plakhov and V.Roshchina gives 2 invisible directions in the plane and 3 in the space. We use reflection group of the root system An in order to make the directions of the roots invisible.

math.DG

On Totally integrable magnetic billiards on constant curvature surface

We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result is a manifestation of the so-called Hopf rigidity phenomenon which was recently obtained for classical billiards on constant curvature surfaces.

math.DS

Smooth solutions for a ${p}$-system of mixed type

In this note we analyze smooth solutions of a $p$-system of the \textit{mixed} type. Motivating example for this is a 2-components reduction of the Benney moments chain which appears to be connected to theory of integrable systems. We don't assume a-priory that the solutions in question are in the Hyperbolic region. Our main result states that the only smooth solutions of the system which are periodic in $x$ are necessarily constants. As for initial value problem we prove that if the initial data is strictly hyperbolic and periodic in $x$ then the solution can not extend to $[t_0;+\infty)$ and shocks are necessarily created.

math.AP

New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

We consider magnetic geodesic flows on the 2-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a Semi-Hamiltonian system of quasi-linear equations, i.e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.

math-ph