Related papers: Testing for separability is hard
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…
Nowadays whenever a user buys any gadget, apart from the price his focus would also be on how easy is the functionality of the gadget. This means users are more concerned towards the usability of the gadget. Therefore, this study set to…
Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, $\mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}$, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda…
Classification tasks are usually analysed and improved through new model architectures or hyperparameter optimisation but the underlying properties of datasets are discovered on an ad-hoc basis as errors occur. However, understanding the…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
Recent studies have shown that the majority of published computational models in systems biology and physiology are not repeatable or reproducible. There are a variety of reasons for this. One of the most likely reasons is that given how…
If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…
We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of $n-1$ particles. The method of providing of the…
Reproducibility, the ability to reproduce the results of published papers or studies using their computer code and data, is a cornerstone of reliable scientific methodology. Studies where results cannot be reproduced by the scientific…
In recent years, an increasing amount of data is collected in different and often, not cooperative, databases. The problem of privacy-preserving, distributed calculations over separated databases and, a relative to it, issue of private data…
We study consumption dependence in the context of random utility and repeated choice. We show that, in the presence of consumption dependence, the random utility model is a misspecified model of repeated rational choice. This…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state \varrho is separable if and only if a specially constructed…
As learning difficulty is crucial for machine learning (e.g., difficulty-based weighting learning strategies), previous literature has proposed a number of learning difficulty measures. However, no comprehensive investigation for learning…
What makes a paper independently reproducible? Debates on reproducibility center around intuition or assumptions but lack empirical results. Our field focuses on releasing code, which is important, but is not sufficient for determining…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
The interleaving distance is arguably the most prominent distance measure in topological data analysis. In this paper, we provide bounds on the computational complexity of determining the interleaving distance in several settings. We show…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…