Related papers: Null Measurability at the Symmetrization Interface…
We develop a unified framework for locating natural properties of algebraic and analytic structures within the Borel hierarchy. Objects are presented as quotients of a universal generator and definability is read directly from the quotient…
Nonlocality, evidenced by the violation of Bell inequalities, not only signifies entanglement but also highlights measurement incompatibility in quantum systems. Utilizing the generalized Clauser-Horne-Shimony-Holt (CHSH) Bell inequality,…
It is known that the topology of a Polish group is uniquely determined by its Borel structure and group operations, but this does not give us a way to find the topology. In this article we expand on this theorem and give a criterion for a…
Continuous perception, the ability to integrate visual observations over time in a continuous stream fashion, is essential for robust real-world understanding, yet remains largely untested in current multimodal models. We introduce…
In tomographic weak lensing surveys, the presence of nulling properties reveals symmetries inherent in the data, which rely solely on the geometrical properties of the Universe. Ensuring its validity thus provides us with constraints on the…
Consider the task of learning a hypothesis class $\mathcal{H}$ in the presence of an adversary that can replace up to an $\eta$ fraction of the examples in the training set with arbitrary adversarial examples. The adversary aims to fail the…
We characterize learnability for quantum measurement classes by establishing matching necessary and sufficient conditions for their PAC learnability, along with corresponding sample complexity bounds, in the setting where the learner is…
In a bipartite Bell scenario involving two local measurements per party and two outcome per measurement, the measurement incompatibility in one wing is both necessary and sufficient to reveal the nonlocality. However, such a one-to-one…
The antisymmetrization of the composite particles in cluster model calculations manifests itself in Pauli forbidden states (ghost states), if one restricts oneself on undeformed cluster in the low energy region. The resonating group method…
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between…
The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…
We consider an average cost stochastic control problem with standard Borel spaces and an unknown transition kernel. We do not assume a parametric structure on the unknown kernel. We present topologies on kernels which lead to their…
Jalali and Poor introduced an asymptotic framework for compressed sensing of stochastic processes, demonstrating that any rate strictly greater than the mean information dimension serves as an upper bound on the number of random linear…
In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…
Objective: Using traditional approaches, a Brain-Computer Interface (BCI) requires the collection of calibration data for new subjects prior to online use. Calibration time can be reduced or eliminated e.g.~by transfer of a pre-trained…
Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…
We propose a novel Generalized Zero-Shot learning (GZSL) method that is agnostic to both unseen images and unseen semantic vectors during training. Prior works in this context propose to map high-dimensional visual features to the semantic…
Test of {macroscopic realism} (MR) is key to understanding the foundation of quantum mechanics. Due to the existence of the {non-invasive measurability} loophole and other interpretation loopholes, however, such test remains an open…
We study a strengthening of the notion of a universally meager set and its dual counterpart that strengthens the notion of a universally null set. We say that a subset $A$ of a perfect Polish space $X$ is countably perfectly meager…
We study measurable dependence of measures on a parameter in the following two classical problems: constructing conditional measures and the Kantorovich optimal transportation. We obtain broad sufficient conditions for the existence of…