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The explosion of activity in finding interactions in complex systems is driven by availability of copious observations of complex natural systems. However, such systems, e.g. the human brain, are rarely completely observable. Interaction network inference must then contend with hidden variables affecting the behavior of the observed parts of the system. We present a novel data-driven approach for model inference with hidden variables. From configurations of observed variables, we identify the observed-to-observed, hidden-to-observed, observed-to-hidden, and hidden-to-hidden interactions, the configurations of hidden variables, and the number of hidden variables. We demonstrate the performance of our method by simulating a kinetic Ising model, and show that our method outperforms existing methods. Turning to real data, we infer the hidden nodes in a neuronal network in the salamander retina and a stock market network. We show that predictive modeling with hidden variables is significantly more accurate than that without hidden variables. Finally, an important hidden variable problem is to find the number of clusters in a dataset. We apply our method to classify MNIST handwritten dig

This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently yields higher rewards compared to the rest. The central question is whether efficient regret minimization algorithms can be designed to discover and exploit such hidden structures, leading to equilibrium in these subgames while maintaining rationality in general. We answer this question affirmatively by developing a composition of regret minimization techniques that achieve optimal external and swap regret bounds. Our approach ensures rapid convergence to correlated equilibria in hidden subgames, leveraging the hidden game structure for improved computational efficiency.

In this paper, we investigate spacetime characterized by a hidden symmetry defined by a given Killing tensor. To exhibit this hidden symmetry, the inverse metric must commute with the Killing tensor under the Schouten-Nijenhuis bracket, which translates into a system of partial differential equations (PDEs) for the inverse metric. For some significant examples, we solve these PDEs directly, deriving spacetimes with prescribed hidden symmetries, including those specified by higher-rank Killing tensors. Utilizing the hidden symmetries, we study related problems such as null geodesics, photon region, and separation of variables of wave equations. Through this work, we aim to demonstrate that hidden symmetry is more accessible than previously believed.

A method is proposed to streamline the computation of hidden particle production rates by factorizing them into i) a model-independent SM contribution, and ii) a observable-independent hidden sector contribution. The Standard Model (SM) contribution can be computed once for each observable and re-used for a wide array of hidden sector models, while the hidden sector contribution can be computed once for each model, and re-used for a wide array of observables. The SM contribution also facilitates extracting model independent constraints on hidden particle production. The method is compatible with effective field theory (EFT) and simplified model approaches. It is illustrated by factorizing the rate of charged kaon decays into a charged lepton and a number of hidden particles, and a single form factor $F_{\ell}$ is found to parametrize the impact of general hidden sectors. We derive model-independent constraints on the form factor $F_e$ that governs decays into positrons and hidden particles.

Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter's thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated. A flavour-free version of the standard model is allowed if the hidden sector is just 30% colder than the observable sector after reheating. Alternatively, if the hidden sector contains a 1-generation version of the standard model with characteristic mass scale below 1 MeV, even identical reheating temperatures are allowed. We then analyze hidden sector freezeout in detail for a concrete model, solving the Boltzmann equation numerically and understanding the results from both observable and hidden sector points of view. We find that WIMPless dark matter indeed obtains the correct relic density for masses in the range keV <

Tor hidden services allow running Internet services while protecting the location of the servers. Their main purpose is to enable freedom of speech even in situations in which powerful adversaries try to suppress it. However, providing location privacy and client anonymity also makes Tor hidden services an attractive platform for every kind of imaginable shady service. The ease with which Tor hidden services can be set up has spurred a huge growth of anonymously provided Internet services of both types. In this paper we analyse the landscape of Tor hidden services. We have studied Tor hidden services after collecting 39824 hidden service descriptors on 4th of Feb 2013 by exploiting protocol and implementation flaws in Tor: we scanned them for open ports; in the case of HTTP services, we analysed and classified their content. We also estimated the popularity of hidden services by looking at the request rate for hidden service descriptors by clients. We found that while the content of Tor hidden services is rather varied, the most popular hidden services are related to botnets.

Hidden spin polarization (HSP) with zero net spin polarization in total but non-zero local spin polarization has been proposed in certain nonmagnetic centrosymmetric compounds, where the individual sectors forming the inversion partners are all inversion asymmetry. Here, we extend this idea to antiferromagnetic materials with $PT$ symmetry (the joint symmetry of space inversion symmetry ($P$) and time-reversal symmetry ($T$)), producing zero net spin polarization in total, but either of the two inversion-partner sectors possesses altermagnetism, giving rise to non-zero local spin polarization in the real space, dubbed "hidden altermagnetism". By first-principle calculations, we predict that $PT$-symmetric bilayer $\mathrm{Cr_2SO}$ can serve as a possible candidate showing altermagnetic HSP. By applying an external electric field to break the global $P$ symmetry, the hidden altermagnetism can be separated and observed experimentally. Our works extend the hidden physics, and will also advance the theoretical and experimental search for new type of spin-polarized materials.

Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration, can be decomposed into an arbitrary number of subsystems. The resulting structure is rich enough to enable quantum computation, violation of Bell's inequalities, and formulation of universal quantum gates. Less standard quantum applications involve a distinction between position and hidden position. The hidden position can be accompanied by a hidden spin, even if the particle is spinless. Hidden degrees of freedom are in many respects analogous to modular variables. Moreover, it is shown that these hidden structures are at the roots of some well known theoretical constructions, such as the Brandt-Greenberg multi-boson representation of creation-annihilation operators, intensively investigated in the context of higher-order or fractional-order squeezing. I

Hidden-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of hidden-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between hidden-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry doublets. If furthermore the kinetic energies of the heavy hadrons are much larger than their spin splittings, we obtain analytic expressions for the relative partial decay rates in terms of Wigner 6-j and 9-j symbols. We consider in detail the decays of quarkonia and quarkonium hybrids into the lightest heavy-meson pairs. For quarkonia, our model-independent selection rules and relative partial decay rat

Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the computation of precision matrices and have a lot of unnecessary parameters. As a consequence, such models often perform better when it is assumed that all variables are independent, a hypothesis that may be unrealistic. Hidden Markov models based on kernel density estimation are also capable of modeling non-Gaussian data, but they assume independence between variables. In this article, we introduce a new hidden Markov model based on kernel density estimation, which is capable of capturing kernel dependencies using context-specific Bayesian networks. The proposed model is described, together with a learning algorithm based on the expectation-maximization algorithm. Additionally, the model is compared to related HMMs on synthetic and real data. From the results, the benefits in likelihood and classification accuracy from the proposed model are quantified and analyzed.

This paper consists of $3$ parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second part, the notion of quantum hidden process is introduced. In the third part it is proven that, by restricting various types of quantum Markov chains to appropriate commutative sub-algebras (diagonal sub-algebras) one recovers all the classical hidden process and, in addition, one obtains families of processes which are not usual hidden Markov process, but are included in the above mentioned extensions of these processes. In this paper we only deal with processes with an at most countable state space.

The Bell theorem is explored in terms of a trade-off relation between underlying assumptions within the hidden variable model framework. In this paper, recognizing the incorporation of hidden variables as one of the fundamental assumptions, we propose a measure termed `hidden information' taking account of their distribution. This measure quantifies the number of hidden variables that essentially contribute to the empirical statistics. For factorizable models, hidden variable models that satisfy `locality' without adhering to the measurement independence criterion, we derive novel relaxed Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequalities. These inequalities elucidate trade-off relations between measurement dependence and hidden information in the CHSH scenario. It is also revealed that the relation gives a necessary and sufficient condition for the measures to be realized by a factorizable model.

Photon entanglement is indispensable for optical quantum technologies. Measurement-based optical quantum computing and all-optical quantum networks rely on multiphoton cluster states consisting of indistinguishable entangled photons. A promising method for creating such cluster states on demand is spin-photon entanglement using the spin of a resident charge carrier in a quantum dot, precessing in a weak external magnetic field. In this work, we show theoretically and experimentally that spin-photon entanglement is strongly affected by the hidden anisotropy of quantum dots, which can arise from mechanical stress, shape anisotropy and even specific crystal structure. In the measurements of time-resolved photoluminescence and cross-polarized second-order photon correlation function in a magnetic field, the anisotropy manifests itself in the spin dynamics and, as a consequence, in the spin-photon concurrence. The measured time-filtered spin-photon Bell state fidelity depends strongly on the excitation polarization and reaches an extremely high value of 94% at maximum. We specify the magnetic field and excitation polarization directions that maximize spin-photon entanglement and thereby

Two protocols are proposed for two closely linked but different variants of remote implementation of quantum operators of specific forms. The first protocol is designed for the remote implementation of the single qubit hidden quantum operator, whereas the second one is designed for the remote implementation of the partially unknown single qubit quantum operator. In both cases two-qubit maximally entangled state, which is entangled in the spatial degree of freedom is used. The quantum resources used here are optimal and easy to realize and maintain in comparison to the multi-partite or multi-mode entangled states used in earlier works. The impact of photon loss due to interaction with the environment is analyzed for both the schemes. The proposed protocols are also generalized to their controlled, bidirectional, cyclic, controlled cyclic, and controlled bidirectional versions and it is shown that either Bell state alone or products of Bell states will be sufficient to perform these tasks with some additional classical communications in the controlled cases only. This is in sharp contrast to the earlier proposals that require large entangled states. In addition, it's noted that remot

Time-series models typically assume untainted and legitimate streams of data. However, a self-interested adversary may have incentive to corrupt this data, thereby altering a decision maker's inference. Within the broader field of adversarial machine learning, this research provides a novel, probabilistic perspective toward the manipulation of hidden Markov model inferences via corrupted data. In particular, we provision a suite of corruption problems for filtering, smoothing, and decoding inferences leveraging an adversarial risk analysis approach. Multiple stochastic programming models are set forth that incorporate realistic uncertainties and varied attacker objectives. Three general solution methods are developed by alternatively viewing the problem from frequentist and Bayesian perspectives. The efficacy of each method is illustrated via extensive, empirical testing. The developed methods are characterized by their solution quality and computational effort, resulting in a stratification of techniques across varying problem-instance architectures. This research highlights the weaknesses of hidden Markov models under adversarial activity, thereby motivating the need for robustif

We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the Hidden Subset Sum Problem, whose hardness is essentially determined by that of the hidden lattice problem. We describe and compare two algorithms for the hidden lattice problem: we first adapt the algorithm by Nguyen and Stern for the hidden subset sum problem, based on orthogonal lattices, and propose a new variant, which we explain to be related by duality in lattice theory. Following heuristic, rigorous and practical analyses, we find that our new algorithm brings some advantages as well as a competitive alternative for algorithms for problems with cryptographic interest, such as Approximate Common Divisor Problems, and the Hidden Subset Sum Problem. Finally, we study variations of the problem and highlight its relevance to cryptanalysis.

In 1964, Lipkin discovered the zilches, a set of conserved quantities in free electromagnetism. Among the zilches, optical chirality was identified by Tang and Cohen in 2010, serving as a measure of the handedness of light and leading to investigations into light's interactions with chiral matter. While the symmetries underlying the conservation of the zilches have been examined, the derivation of zilch conservation laws from symmetries of the standard free electromagnetic (EM) action using Noether's theorem has only been addressed in the case of optical chirality. We provide the full answer by demonstrating that the zilch symmetry transformations of the four-potential, $A_μ$, preserve the standard free EM action. We also show that the zilch symmetries belong to the enveloping algebra of a "hidden" invariance algebra of free Maxwell's equations. This "hidden" algebra is generated by familiar conformal transformations and certain "hidden" symmetry transformations of $A_μ$. Generalizations of the ``hidden'' symmetries are discussed in the presence of a material four-current, as well as in the theory of a complex Abelian gauge field. Additionally, we extend the zilch symmetries of the

Various extensions of the Standard Model predict the existence of hidden photons kinetically mixing with the ordinary photon. This mixing leads to oscillations between photons and hidden photons, analogous to the observed oscillations between different neutrino flavors. In this context, we derive new bounds on the photon-hidden photon mixing parameters using the high precision cosmic microwave background spectral data collected by the Far Infrared Absolute Spectrophotometer instrument on board of the Cosmic Background Explorer. Requiring the distortions of the CMB induced by the photon-hidden photon mixing to be smaller than experimental upper limits, this leads to a bound on the mixing angle < 10^{-7}-10^{-5} for hidden photon masses between 10^{-14} eV and 10^{-7} eV. This low-mass and low-mixing region of the hidden photon parameter space was previously unconstrained.

A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the relations to other variables in the model and determining the number of states of the hidden variable. In this paper, we address the latter problem in the context of Bayesian networks. We describe an approach that utilizes a score-based agglomerative state-clustering. As we show, this approach allows us to efficiently evaluate models with a range of cardinalities for the hidden variable. We show how to extend this procedure to deal with multiple interacting hidden variables. We demonstrate the effectiveness of this approach by evaluating it on synthetic and real-life data. We show that our approach learns models with hidden variables that generalize better and have better structure than previous approaches.