Information-theoretic Analysis Research Articles

Non-Markov models of single-molecule dynamics from information-theoretical analysis of trajectories.

Whether single-molecule trajectories, observed experimentally or in molecular simulations, can be described using simple models such as biased diffusion is a subject of considerable debate. Memory effects and anomalous diffusion have been reported in a number of studies, but directly inferring such effects from trajectories, especially given limited temporal and/or spatial resolution, has been a challenge. Recently, we proposed that this can be achieved with information-theoretical analysis of trajectories, which is based on the general observation that non-Markov effects make trajectories more predictable and, thus, more "compressible" by lossless compression algorithms. Toy models where discrete molecular states evolve in time were shown to be amenable to such analysis, but its application to continuous trajectories presents a challenge: the trajectories need to be digitized first, and digitization itself introduces non-Markov effects that depend on the specifics of how trajectories are sampled. Here we develop a milestoning-based method for information-theoretical analysis of continuous trajectories and show its utility in application to Markov and non-Markov models and to trajectories obtained from molecular simulations.

Negation of a probability distribution: An information theoretic analysis

Yager (2014) proposed a transformation for negating the happening of an uncertain event which opposes the occurrence of any uncertain event by redistributing its probability equally among the other outcomes. Yager’s negation applied repeatedly on any probability distribution converges to the uniform distribution (all events having identical probability of occurrence). In most cases, uniform distribution is the maximum entropy probability distribution (MEPD) as it has maximum uncertainty inherent in it. However, if some information is available regarding the occurrence of events associated with a random experiment, then MEPD may or may not be a uniform distribution. In this work, we have first explored some new properties of Yager’s negation and then investigated Yager’s negation when we have some additional information about the probability distribution other than the natural constraints. The MEPD in the presence of this additional information is determined using the negation of probabilities. It is shown that the existence of MEPD (and as a result the maximum entropy) largely depends on the parameters of the additional constraints. Some numerical examples have been considered for comparing the MEPD with and without additional constraints.

On the relation between the subadditivity cone and the quantum entropy cone

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.

A discriminative information-theoretical analysis of the regularity gradient in inflectional morphology

Over the last decades, several independent lines of research in morphology have questioned the hypothesis of a direct correspondence between sublexical units and their mental correlates. Word and paradigm models of morphology shifted the fundamental part-whole relation in an inflection system onto the relation between individual inflected word forms and inflectional paradigms. In turn, the use of artificial neural networks of densely interconnected parallel processing nodes for morphology learning marked a radical departure from a morpheme-based view of the mental lexicon. Lately, in computational models of Discriminative Learning, a network architecture has been combined with an uncertainty reducing mechanism that dispenses with the need for a one-to-one association between formal contrasts and meanings, leading to the dissolution of a discrete notion of the morpheme.The paper capitalises on these converging lines of development to offer a unifying information-theoretical, simulation-based analysis of the costs incurred in processing (ir)regularly inflected forms belonging to the verb systems of English, German, French, Spanish and Italian. Using Temporal Self-Organising Maps as a computational model of lexical storage and access, we show that a discriminative, recurrent neural network, based on Rescorla-Wagner’s equations, can replicate speakers’ exquisite sensitivity to widespread effects of word frequency, paradigm entropy and morphological (ir)regularity in lexical processing. The evidence suggests an explanatory hypothesis linking Word and paradigm morphology with principles of information theory and human perception of morphological structure. According to this hypothesis, the ways more or less regularly inflected words are structured in the mental lexicon are more related to a reduction in processing uncertainty and maximisation of predictive efficiency than to economy of storage.

Information-theoretic Analysis of Longitude Distribution of Photospheric Magnetic Fields from MDI/HMI Synoptic Maps: Evidence for Rossby Waves

Much of the research on the magnetic activity of the Sun has been focused on its axisymmetric component. However, the longitudinal complexity plays a fundamental role in the solar magnetic activity. Rossby waves have recently been proposed as a fundamental mechanism regarding the nonaxisymmetric nature of the solar magnetic fields. Here, we use HMI and MDI magnetic field synoptic maps to evaluate the magnetic field structures’ (mainly active regions) organization and propagation as a function of time and latitude. We demonstrate, using information theory, that the organization of longitudinal structures observed on synoptic maps is proportional to the level of activity at a given latitude. We further show that this organization on the longitudinal structures is persistent and due to long-lived features. The drift velocity of these long-lived photospheric features is inferred and is shown to significantly vary with latitude, and is compatible with the phase speed of tachocline magnetic Rossby waves with a toroidal field in the range of 5–10 kG. Our results suggest that Rossby waves contribute to the organization and propagation of photospheric magnetic features on the timescale of several months and beyond.

An information theoretic Bayesian uncertainty analysis of AEM systems over Menindee Lake, Australia

SUMMARY Long-range, active-source airborne electromagnetic (AEM) systems for near-surface conductivity imaging fall into two categories: helicopter (rotary-wing) borne or fixed-wing aircraft borne. A multitude of factors such as flying height, transmitter loop area and current, source waveforms, aerodynamic stability and data stacking times contribute to the geological resolvability of the subsurface. A comprehensive comparison of the relative merits of each system considering all such factors is difficult, but test flights over well-constrained subsurface geology with downhole induction logs are extremely useful for resolution studies. However, given the non-linear nature of the electromagnetic inverse problem, handling transmitter–receiver geometries in fixed-wing aircraft is especially challenging. As a consequence of this non-linearity, inspecting the closeness of downhole conductivities to deterministic inversion results is not sufficient for studying resolvability. A more comprehensive picture is provided by examining the variation in probability mass of the depth-wise Bayesian posterior conductivity distributions for each kind of AEM system within an information theoretic framework. For this purpose, probabilistic inversions of data must be carried out. Each acquiring system should fly over the same geology, survey noise levels must be measured and the same prior probabilities on conductivity must be used. With both synthetic models as well as real data from over the Menindee calibration range in New South Wales, Australia, we shed new light on the matter of AEM inverse model uncertainty. We do this using two information theoretic attributes derived from different Kullback–Leibler divergences—Bayesian information gain, and a strictly proper scoring rule, to assess posterior probabilities estimated by a novel Bayesian inversion scheme. The inversion marginalizes fixed-wing geometry attributes as generic nuisance parameters during Markov chain sampling. This is the first time-domain AEM study we know of, that compares nuisance marginalized subsurface posterior conductivities from a fixed-wing system, with rotary-wing derived posterior conductivities. We also compare field results with induction log data where available. Finally, we estimate the information gain in each case via a covariate shift adaptation technique that has not been used before in geophysical work. Our findings have useful implications in AEM system selection, as well as in the design of better deterministic AEM inversion algorithms.

A nonbinary LDPC-coded product distribution matching probabilistic shaping scheme for high order modulation

In this paper, a non-binary low-density parity-check (LDPC)-coded low complexity product distribution matching (PDM) probabilistic shaping (PS) scheme for high-order modulation is proposed. Compared with conventional non-binary LDPC-coded regular quadrature amplitude modulation (QAM) schemes, the proposed non-binary LDPC-coded low complexity PDM-PS QAM scheme can obtain shaping gain, as evidenced through theoretical average mutual information and simulated error performance analyses. When the spectral efficiency is 4.5 bits/s/Hz, compared with the regular 64QAM system, the proposed 64QAM PDM-PS system can obtain 0.26 dB theoretical energy gain, while its simulated error performance is 0.30 dB. When the spectral efficiency is 6.0 bits/s/Hz, compared with the regular 256QAM system, the proposed 256QAM PDM-PS system can obtain 0.73 dB theoretical energy gain, while its simulated error performance is 0.93 dB. Compared with the conventional non-binary LDPC-coded PS QAM scheme, the proposed non-binary LDPC-coded PDM-PS QAM scheme can reduce the computational complexity by 33.1% and 49.7% under 64QAM and 256QAM, respectively, with acceptable error performance loss. The information-theoretic and error performance analyses both indicate the effectiveness and reliability of the proposed scheme.

Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis

The stability of a two-electron Zee system trapped inside an impenetrable spherical cavity is analyzed using an explicitly correlated multi-exponent Hylleraas-type basis set in the framework of the Ritz variational method. The wave function is considered to be consistent with Dirichlet’s boundary condition. Four different values are considered, where denotes the critical nuclear charge beyond which the system is embedded in a discrete positive energy continuum due to the impenetrable nature of the cavity. The energy contribution due to the total correlation (in the presence of both radial and angular correlation) effect, the radial correlation limit, and the angular correlation limit are also studied in detail. The thermodynamic pressure felt by the two-electron Zee system inside the cavity is estimated, and a formula replicating the behavior between the pressure and volume of the cavity is deduced by a fitting procedure. Different geometrical properties, e.g. radial moments (, , , , ; p = ), angular moments (, ), and related important physical quantities, are determined. The variation of Kirkwood and Buckingham polarizabilities w.r.t. the pressure felt by the two-electron Zee system is analyzed. A one-electron radial density is estimated for each pair of (), which has been employed to generate the electrostatic potential as well as different information theoretical measures like Shannon entropy, Fisher entropy, Rényi entropy, Tsallis entropy, and Onicescu informational energy. The chosen information theoretical measures have been found to be sensitive tools for describing changes in the electronic structure due to spatial confinement. An interesting interplay between the electronic and nuclear contribution to the classical electrostatic potential is observed, leading to a shift in the position of its characteristic minimum due to compression. Wherever possible, a comparison is made in order to ascertain the high accuracy of our numerical results. The procedure of analytic evaluation of the integrals needed to estimate the atomic properties under consideration is discussed in detail.

Phenomenological description of the acidity of the citric acid and its deprotonated species: informational-theoretical study.

In spite of the fact that molecular acidity is a fundamental physicochemical property of molecular systems, the vast majority of theoretical studies have focused attention on monoprotic acids and on the prediction of pKa's. Polyprotic acids, represent a challenge for electronic structure calculations since the multiple acidic sites result in a vast group of species with different conformations and reactivities. In this work, Information-theoretic (IT) concepts of localizability, order and uniformity are applied to the Citric Acid and its deprotonated species through the one-electron density functionals: Shannon entropy (S), Fisher information (I) and Disequilibrium (D), respectively. We pursue the goal of characterizing the acidity of the aforementioned species with the aim to associate the IT concepts to chemical features such as the polarizability of the protonated/deprotonated species, the liability of the acidic sites, atomic electrostatic potentials, covalent bonding. IT analyses looks very promising for future studies on the acidity of specific deprotonation-sites of polyprotic acids. Density functional theory (DFT) calculations were performed with Gaussian 09 program. A sensitivity analysis of the IT-measures was performed for the citric acid and the citrate using B3LYP, B3PW91, BPW91, M05-2X, M06-2X and PBEPBE functionals with the 6-311++g(3df,2p), 6-311++g(d,p), 6.311+g(d,p) and aug-cc-pVDZ basis sets. The rest of the analysis was performed with the M05-2X/6-311+G(d,p) level of theory. Additionally, aqueous media was considered by use of the SMD solvent model. The IT-measures were calculated using a suite of programs developed in our laboratory jointly with the DGRID software package.

Information-Theoretic Analysis of Cardio-Respiratory Interactions in Heart Failure Patients: Effects of Arrhythmias and Cardiac Resynchronization Therapy.

The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy.

An information-theoretic analysis of resting-state versus task fMRI.

Resting-state fMRI is an increasingly popular alternative to task-based fMRI. However, a formal quantification of the amount of information provided by resting-state fMRI as opposed to active task conditions about neural responses is lacking. We conducted a systematic comparison of the quality of inferences derived from a resting-state and a task fMRI paradigm by means of Bayesian Data Comparison. In this framework, data quality is formally quantified in information-theoretic terms as the precision and amount of information provided by the data on the parameters of interest. Parameters of effective connectivity, estimated from the cross-spectral densities of resting-state- and task time series by means of dynamic causal modelling (DCM), were subjected to the analysis. Data from 50 individuals undergoing resting-state and a Theory-of-Mind task were compared, both datasets provided by the Human Connectome Project. A threshold of very strong evidence was reached in favour of the Theory-of-Mind task (>10 bits or natural units) regarding information gain, which could be attributed to the active task condition eliciting stronger effective connectivity. Extending these analyses to other tasks and cognitive systems will reveal whether the superior informative value of task-based fMRI observed here is case specific or a more general trend.

Information-theoretic analysis of Hierarchical Temporal Memory-Spatial Pooler algorithm with a new upper bound for the standard information bottleneck method.

Hierarchical Temporal Memory (HTM) is an unsupervised algorithm in machine learning. It models several fundamental neocortical computational principles. Spatial Pooler (SP) is one of the main components of the HTM, which continuously encodes streams of binary input from various layers and regions into sparse distributed representations. In this paper, the goal is to evaluate the sparsification in the SP algorithm from the perspective of information theory by the information bottleneck (IB), Cramer-Rao lower bound, and Fisher information matrix. This paper makes two main contributions. First, we introduce a new upper bound for the standard information bottleneck relation, which we refer to as modified-IB in this paper. This measure is used to evaluate the performance of the SP algorithm in different sparsity levels and various amounts of noise. The MNIST, Fashion-MNIST and NYC-Taxi datasets were fed to the SP algorithm separately. The SP algorithm with learning was found to be resistant to noise. Adding up to 40% noise to the input resulted in no discernible change in the output. Using the probabilistic mapping method and Hidden Markov Model, the sparse SP output representation was reconstructed in the input space. In the modified-IB relation, it is numerically calculated that a lower noise level and a higher sparsity level in the SP algorithm lead to a more effective reconstruction and SP with 2% sparsity produces the best results. Our second contribution is to prove mathematically that more sparsity leads to better performance of the SP algorithm. The data distribution was considered the Cauchy distribution, and the Cramer-Rao lower bound was analyzed to estimate SP's output at different sparsity levels.

Characterizing neural coding performance for populations of sensory neurons: comparing a weighted spike distance metrics to other analytical methods.

The identity of sensory stimuli is encoded in the spatio-temporal patterns of responses of the encoding neural population. For stimuli to be discriminated reliably, differences in population responses must be accurately decoded by downstream networks. Several methods to compare patterns of responses have been used by neurophysiologists to characterize the accuracy of the sensory responses studied. Among the most widely used analyses, we note methods based on Euclidean distances or on spike metric distances. Methods based on artificial neural networks and machine learning that recognize and/or classify specific input patterns have also gained popularity. Here, we first compare these three strategies using datasets from three different model systems: the moth olfactory system, the electrosensory system of gymnotids, and leaky-integrate-and-fire (LIF) model responses. We show that the input-weighting procedure inherent to artificial neural networks allows the efficient extraction of information relevant to stimulus discrimination. To combine the convenience of methods such as spike metric distances but leverage the advantages of weighting the inputs, we propose a measure based on geometric distances where each dimension is weighted proportionally to how informative it is. We show that the result of this Weighted Euclidian Distance (WED) analysis performs as well or better than the artificial neural network we tested and outperforms the more traditional spike distance metrics. We applied information theoretic analysis to LIF responses and compared their encoding accuracy with the discrimination accuracy quantified through this WED analysis. We show a high degree of correlation between discrimination accuracy and information content, and that our weighting procedure allowed the efficient use of information present to perform the discrimination task. We argue that our proposed measure provides the flexibility and ease of use sought by neurophysiologists while providing a more powerful way to extract relevant information than more traditional methods.

Less is more in language production: an information-theoretic analysis of agrammatism in primary progressive aphasia.

Agrammatism is a disorder of language production characterized by short, simplified sentences, the omission of function words, an increased use of nouns over verbs and a higher use of heavy verbs. Despite observing these phenomena for decades, the accounts of agrammatism have not converged. Here, we propose and test the hypothesis that the lexical profile of agrammatism results from a process that opts for words with a lower frequency of occurrence to increase lexical information. Furthermore, we hypothesize that this process is a compensatory response to patients' core deficit in producing long, complex sentences. In this cross-sectional study, we analysed speech samples of patients with primary progressive aphasia (n = 100) and healthy speakers (n = 65) as they described a picture. The patient cohort included 34 individuals with the non-fluent variant, 41 with the logopenic variant and 25 with the semantic variant of primary progressive aphasia. We first analysed a large corpus of spoken language and found that the word types preferred by patients with agrammatism tend to have lower frequencies of occurrence than less preferred words. We then conducted a computational simulation to examine the impact of word frequency on lexical information as measured by entropy. We found that strings of words that exclude highly frequent words have a more uniform word distribution, thereby increasing lexical entropy. To test whether the lexical profile of agrammatism results from their inability to produce long sentences, we asked healthy speakers to produce short sentences during the picture description task. We found that, under this constrained condition, a similar lexical profile of agrammatism emerged in the short sentences of healthy individuals, including fewer function words, more nouns than verbs and more heavy verbs than light verbs. This lexical profile of short sentences resulted in their lower average word frequency than unconstrained sentences. We extended this finding by showing that, in general, shorter sentences get packaged with lower-frequency words as a basic property of efficient language production, evident in the language of healthy speakers and all primary progressive aphasia variants.

Information transport and limits of optical imaging in the highly diffusive regime

Noninvasive imaging through the human body or dense fog at optical wavelengths requires the collection of highly scattered photons, which corrupt imaging information and restrict most diffuse imaging techniques to $<$ 10 transport mean free path (TMFP) lengths. An information theoretical analysis of numerical simulations including practical considerations shows imaging information exists at the single-photon detection limit beyond 200 TMFP lengths. Information can be enhanced through increasing the collection of light, optimizing detector placement, and resolving measurements in the space-time domain.

Information-theoretical analysis of statistical measures for multiscale dynamics.

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields, their interest lies in examining the multiscale temporal structures of physical phenomena under study. We demonstrate that from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, natural physical systems including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence, the MSE and Allan variance demonstrate similar properties. As a counterexample, we demonstrate an artificially constructed random sequence, for which the MSE and Allan variance exhibit different trends.

Lossy State Communication over Fading Multiple Access Channels.

Joint communications and sensing functionalities integrated into the same communication network have become increasingly relevant due to the large bandwidth requirements of next-generation wireless communication systems and the impending spectral shortage. While there exist system-level guidelines and waveform design specifications for such systems, an information-theoretic analysis of the absolute performance capabilities of joint sensing and communication systems that take into account practical limitations such as fading has not been addressed in the literature. Motivated by this, we undertake a network information-theoretic analysis of a typical joint communications and sensing system in this paper. Towards this end, we consider a state-dependent fading Gaussian multiple access channel (GMAC) setup with an additive state. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and non-causally available to all the transmitting nodes. The fading gains on the respective links are assumed to be stationary and ergodic and available only at the receiver. In this setting, with no knowledge of fading gains at the transmitters, we are interested in joint message communication and estimation of the state at the receiver to meet a target distortion in the mean-squared error sense. Our main contribution here is a complete characterization of the distortion-rate trade-off region between the communication rates and the state estimation distortion for a two-sender GMAC. Our results show that the optimal strategy is based on static power allocation and involves uncoded transmissions to amplify the state, along with the superposition of the digital message streams using appropriate Gaussian codebooks and dirty paper coding (DPC). This acts as a design directive for realistic systems using joint sensing and transmission in next-generation wireless standards and points to the relative benefits of uncoded communications and joint source-channel coding in such systems.

Functional and mechanistic diversity in ant tandem communication

Communication is fundamental to the organization of animal societies, often resulting in the convergent evolution of similar social behavior across lineages. However, this similarity may conceal underlying functional and mechanistic differences. Here we combined network and information-theoretic analysis to quantify how tandem recruitment is distinguishable between two ant genera, Temnothorax and Diacamma. We show that Temnothorax uses tandem running to recruit additional recruiters, while Diacamma uses it principally to move the passive majority of their colony, a task that Temnothorax accomplishes with a different behavior, social carrying. Accordingly, the network structure of Diacamma tandems was dissimilar to that of Temnothorax, instead resembling the social-carrying networks in Temnothorax. Furthermore, our information-theoretical analysis on movement trajectories revealed that Diacamma tandem runs lack bidirectional information transfer, the signature of route learning in Temnothorax. By quantifying the diversity of similar communication systems, this study increases the resolution of our understanding of animal societies.

Computing the Integrated Information of a Quantum Mechanism.

Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT's latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that end, we translate a recently developed, unique measure of intrinsic information into a density matrix formulation and extend the notion of conditional independence to accommodate quantum entanglement. The compositional nature of the IIT analysis might shed some light on the internal structure of composite quantum states and operators that cannot be obtained using standard information-theoretical analysis. Finally, our results should inform theoretical arguments about the link between consciousness, causation, and physics from the classical to the quantum.

Cramér–Rao, Fisher–Shannon and LMC–Rényi Complexity-like Measures of Multidimensional Hydrogenic Systems with Application to Rydberg States

Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by means of the monotone complexity measures of Cramér–Rao, Fisher–Shannon and LMC(Lopez-Ruiz, Mancini, Calbet)–Rényi types. These quantities are shown to be analytically determined from first principles, i.e., explicitly in terms of the space dimensionality D, the nuclear charge and the hyperquantum numbers, which characterize the system’ states. Then, they are applied to several relevant classes of particular states with emphasis on the quasi-spherical and the highly excited Rydberg states, obtaining compact and physically transparent expressions. This is possible because of the use of powerful techniques of approximation theory and orthogonal polynomials, asymptotics and generalized hypergeometric functions.