Related papers: Sensitivity and block sensitivity of nested canaly…

The relative performance of competing point forecasts is usually measured in terms of loss or scoring functions. It is widely accepted that these scoring function should be strictly consistent in the sense that the expected score is…

Background: An electron localization function was originally introduced to visualize bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules and solids. In nuclear physics, a nucleon…

Any simulation of the r-process is affected by uncertainties in our present knowledge of nuclear physics quantities and astrophysical conditions. It is common to quantify the impact of these uncertainties through a global sensitivity…

We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although…

The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…

There is a fundamental limit on the capacity of fibre optical communication system (Shannon Limit). This limit can be potentially overcome via using Nonlinear Frequency Division Multiplexing. Dealing with noises in these systems is one of…

This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed that only one…

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…

A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…

This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper…

Nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32^4 (\simeq (4.4 fm)^4) lattice. A NN potential V_{NN}(r) is defined from…

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…

Existing learning methods often struggle to balance interpretability and predictive performance. While models like nearest neighbors and non-negative matrix factorization (NMF) offer high interpretability, their predictive performance on…

We establish new separations between the power of monotone and general (non-monotone) Boolean circuits: - For every $k \geq 1$, there is a monotone function in ${\sf AC^0}$ that requires monotone circuits of depth $\Omega(\log^k n)$. This…

With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known…

For any Boolean function $f:\{0,1\}^n \to \{0,1\}$ with a complexity measure having value $k \ll n$, is it possible to restrict the function $f$ to $\Theta(k)$ variables while keeping the complexity preserved at $\Theta(k)$? This question,…

In this letter, we present the frequency dependence of the vortex surface resistance of bulk niobium accelerating cavities as a function of different state-of-the-art surface treatments. Higher flux surface resistance per amount of trapped…

The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that the problems of the sensitivity parameter are almost identical to the…

Memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol insertions and deletions in addition to random errors are considered. Such channels are information stable, hence their Shannon…