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Probabilistic generative neural networks are useful for many applications, such as image classification, speech recognition and occlusion removal. However, the power budget for hardware implementations of neural networks can be extremely…
A finite set of quantum observables (positive operator valued measures) is called compatible if these observables are marginals of a some observable, called a joint observable of them. For a given set of compatible observables, their joint…
The predicament in semi-supervised few-shot learning (SSFSL) is to maximize the value of the extra unlabeled data to boost the few-shot learner. In this paper, we propose a Poisson Transfer Network (PTN) to mine the unlabeled information…
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent…
Model selection consistency in the high-dimensional regression setting can be achieved only if strong assumptions are fulfilled. We therefore suggest to pursue a different goal, which we call a minimal class of models. The minimal class of…
Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and subsequent states. In this paper, to reduce the complexity of checking the detectability properties in the…
World Health Organization (WHO) provides the guideline for managing the Particulate Matter (PM) level because when the PM level is higher, it threats the human health. For managing PM level, the procedure for measuring PM value is needed…
Let $H^{[ N]}=H^{[ d_{1}]}\otimes ... \otimes H^{[ d_{n}]}$ be a tensor product of Hilbert spaces and let $\tau_{0}$ be the closest separable state in the Hilbert-Schmidt norm to an entangled state $\rho_{0}$. Let $\tilde{\tau}_{0}$ denote…
The class of port-Hamiltonian systems incorporates many physical models, such as mechanical systems in the finite-dimensional case and wave and beam equations in the infinite-dimensional case. In this paper we study a subclass of linear…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…
Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem…
For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic…
Bayesian Belief Networks (BBNs) are a powerful formalism for reasoning under uncertainty but bear some severe limitations: they require a large amount of information before any reasoning process can start, they have limited contradiction…
Detecting small, densely distributed objects is a significant challenge: small objects often contain less distinctive information compared to larger ones, and finer-grained precision of bounding box boundaries are required. In this paper,…
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…
In this paper, a new definition of observability is introduced for PDEs. It is a quantitative measure of partial observability. The quantity is proved to be consistent if approximated using well posed approximation schemes. A first order…
This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…
We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is…
In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, their generation is still problematic. The…
We study the closeness of an experimental unitary bosonic network with only partially indistinguishable bosons in an arbitrary mixed input state, in particular an experimental realization of the Boson Sampling, to the ideal bosonic network,…