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In visual scene understanding tasks, it is essential to capture both invariant and equivariant structure. While neural networks are frequently trained to achieve invariance to transformations such as translation, this often comes at the…

As robots perform manipulation tasks and interact with objects, it is probable that they accidentally drop objects (e.g., due to an inadequate grasp of an unfamiliar object) that subsequently bounce out of their visual fields. To enable…

We consider the minimum-norm-point (MNP) problem over polyhedra, a well-studied problem that encompasses linear programming. We present a general algorithmic framework that combines two fundamental approaches for this problem: active set…

When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might be a liquid film or an arrangement of…

We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…

Matrix-product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method…

We study separable system-environment evolutions of pure dephasing type in the context of objectivity and find that it can lead to the natural emergence of Spectrum Broadcast Structure (SBS) states at discrete instances of time. Contrary to…

Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of direction constraints between the points is equivalent to the…

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…

Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…

Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…

Camouflaged object detection is an emerging and challenging computer vision task that requires identifying and segmenting objects that blend seamlessly into their environments due to high similarity in color, texture, and size. This task is…

The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…

We introduce a non-interacting boson model to investigate topological structure of complex networks in the present paper. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important…

This paper addresses the problem of contact-based manipulation of deformable linear objects (DLOs) towards desired shapes with a dual-arm robotic system. To alleviate the burden of high-dimensional continuous state-action spaces, we model…

In order to manipulate a deformable object, such as rope or cloth, in unstructured environments, robots need a way to estimate its current shape. However, tracking the shape of a deformable object can be challenging because of the object's…

We present, as a very general method, an effective field theory to analyze models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it gives the exact…

Motion reasoning serves as the cornerstone of multi-object tracking (MOT), as it enables consistent association of targets across frames. However, existing motion estimation approaches face two major limitations: (1) instability caused by…

We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits…