Parameter-free Version Research Articles

Multi-View Adjacency-Constrained Hierarchical Clustering

This paper explores the problem of multi-view clustering, which aims to promote clustering performance with multi-view data. The majority of existing methods have problems with parameter adjustment and high computational complexity. Moreover, in the past, there have been few works based on hierarchical clustering to learn the granular information of multiple views. To overcome these limitations, we propose a simple but efficient framework: Multi-view adjacency-Constrained Hierarchical Clustering (MCHC). Specifically, MCHC mainly consists of three parts: including the Fusion Distance matrices with Extreme Weights (FDEW); adjacency-Constrained Nearest Neighbor Clustering (CNNC); and the internal evaluation Index based on Rawls' Max-Min criterion (MMI). FDEW aims to learn a fusion distance matrix set, which not only uses complementary information among multiple views, but exploits the information from each single view. CNNC is utilized to generate multiple partitions based on FDEW, and MMI is designed for choosing the best one from the multiple partitions. In addition, we propose a parameter-free version of MCHC (MCHC-PF). Without any parameter selection, MCHC-PF can give partitions at different granularity levels with a low time complexity. Comprehensive experiments tested on eight real-world datasets validate the superiority of the proposed methods compared with the 13 current state-of-the-art methods.

Stardust: improving spatial transcriptomics data analysis through space-aware modularity optimization-based clustering.

BackgroundSpatial transcriptomics (ST) combines stained tissue images with spatially resolved high-throughput RNA sequencing. The spatial transcriptomic analysis includes challenging tasks like clustering, where a partition among data points (spots) is defined by means of a similarity measure. Improving clustering results is a key factor as clustering affects subsequent downstream analysis. State-of-the-art approaches group data by taking into account transcriptional similarity and some by exploiting spatial information as well. However, it is not yet clear how much the spatial information combined with transcriptomics improves the clustering result.ResultsWe propose a new clustering method, Stardust, that easily exploits the combination of space and transcriptomic information in the clustering procedure through a manual or fully automatic tuning of algorithm parameters. Moreover, a parameter-free version of the method is also provided where the spatial contribution depends dynamically on the expression distances distribution in the space. We evaluated the proposed methods results by analyzing ST data sets available on the 10x Genomics website and comparing clustering performances with state-of-the-art approaches by measuring the spots' stability in the clusters and their biological coherence. Stability is defined by the tendency of each point to remain clustered with the same neighbors when perturbations are applied.Conclusions Stardust is an easy-to-use methodology allowing to define how much spatial information should influence clustering on different tissues and achieving more stable results than state-of-the-art approaches.

Multi-View Adjacency-Constrained Nearest Neighbor Clustering (Student Abstract)

Most existing multi-view clustering methods have problems with parameter selection and high computational complexity, and there have been very few works based on hierarchical clustering to learn the complementary information of multiple views. In this paper, we propose a Multi-view Adjacency-constrained Nearest Neighbor Clustering (MANNC) and its parameter-free version (MANNC-PF) to overcome these limitations. Experiments tested on eight real-world datasets validate the superiority of the proposed methods compared with the 13 current state-of-the-art methods.

Partial Exchangeability for Contingency Tables

A parameter free version of classical models for contingency tables is developed along the lines of de Finetti’s notions of partial exchangeability.

Parameter-free description of the manifold of non-degenerate density matrices

The paper gives a definition of exponential arcs in the manifold of non-degenerate density matrices and uses it as a starting point to develop a parameter-free version of non-commutative Information Geometry in the finite-dimensional case. Given the Bogoliubov metric, the m- and e-connections are each other dual. Convex potentials are introduced. They allow to introduce dual charts. Affine coordinates are introduced at the end to make the connection with the more usual approach.

Underground test of gravity-related wave function collapse

Roger Penrose proposed that a spatial quantum superposition collapses as a back-reaction from spacetime, which is curved in different ways by each branch of the superposition. In this sense, one speaks of gravity-related wave function collapse. He also provided a heuristic formula to compute the decay time of the superposition—similar to that suggested earlier by Lajos Diósi, hence the name Diósi–Penrose model. The collapse depends on the effective size of the mass density of particles in the superposition, and is random: this randomness shows up as a diffusion of the particles’ motion, resulting, if charged, in the emission of radiation. Here, we compute the radiation emission rate, which is faint but detectable. We then report the results of a dedicated experiment at the Gran Sasso underground laboratory to measure this radiation emission rate. Our result sets a lower bound on the effective size of the mass density of nuclei, which is about three orders of magnitude larger than previous bounds. This rules out the natural parameter-free version of the Diósi–Penrose model.

Adaptive Kendall's Correlation in Bipartite Network for Recommendation

The commonly used algorithms in recommender system tend to recommend popular items. The recently proposed algorithm, denoted as G-CosRA, shows good performance in handling this problem, with two parameters to control the popularity of items and activeness of users. In this paper, we refine this algorithm and propose a new recommendation algorithm based on adaptive Kendall’s τ correlation, where only one tuning parameter is involved. The proposal has better performance in accuracy, popularity and diversity, compared with G-CosRA and other existing algorithms. A parameter-free version, named weighted Kendall, is also proposed for better efficiency in computing.

Parameter-free driven Liouville-von Neumann approach for time-dependent electronic transport simulations in open quantum systems

A parameter-free version of the recently developed driven Liouville-von Neumann equation [T. Zelovich et al., J. Chem. Theory Comput. 10(8), 2927–2941 (2014)] for electronic transport calculations in molecular junctions is presented. The single driving rate, appearing as a fitting parameter in the original methodology, is replaced by a set of state-dependent broadening factors applied to the different single-particle lead levels. These broadening factors are extracted explicitly from the self-energy of the corresponding electronic reservoir and are fully transferable to any junction incorporating the same lead model. The performance of the method is demonstrated via tight-binding and extended Hückel calculations of simple junction models. Our analytic considerations and numerical results indicate that the developed methodology constitutes a rigorous framework for the design of “black-box” algorithms to simulate electron dynamics in open quantum systems out of equilibrium.

Dynamical mean field theory for diatomic molecules and the exact double counting

Dynamical mean field theory (DMFT) combined with the local density approximation (LDA) is widely used in solids to predict properties of correlated systems. In this study, a parameter-free version of the LDA+DMFT framework is implemented and tested on one of the simplest strongly correlated systems, the ${\text{H}}_{2}$ molecule. Specifically, we propose a method to calculate the exact intersection of LDA and DMFT that leads to highly accurate subtraction of the doubly counted correlation in both methods. When the exact-double-counting treatment and a good projector to the correlated subspace are used, LDA+DMFT yields a very accurate total energy and excitation spectrum of ${\text{H}}_{2}$. We also discuss how this double-counting scheme can be extended to solid state calculations.

Nearly universal consistency of maximum likelihood in discrete models

The consistency of the maximum likelihood estimator (MLE) has been well studied in many papers such as Wald (1949), Kiefer and Wolfowitz (1956) and many more subsequent works. The purpose of this short note is to provide a new direction to understand the consistency of the MLE in discrete models. In addition, our work gives a very general and direct proof for the consistency of the MLE by introducing a parameter-free version of consistency.

Operational closure and stability

In this article we introduce and study the notion of operational closure: a transitive set d is called operationally closed iff it contains all constants of OST and any operation f∈d applied to an element a∈d yields an element fa∈d, provided that f applied to a has a value at all. We will show that there is a direct relationship between operational closure and stability in the sense that operationally closed sets behave like Σ1 substructures of the universe. This leads to our final result that OST plus the axiom (OLim), claiming that any set is element of an operationally closed set, is proof-theoretically equivalent to the system KP+(Σ1-Sep) of Kripke–Platek set theory with infinity and Σ1 separation. We also characterize the system OST plus the existence of one operationally closed set in terms of Kripke–Platek set theory with infinity and a parameter-free version of Σ1 separation.

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: Applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.

DENSITY FUNCTIONAL APPROXIMATION FOR NON-HARD SPHERE FLUIDS SUBJECTED TO EXTERNAL FIELDS

A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard–Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.

Polymer density functional theory approach based on scaling second-order direct correlation function

A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

Local Solvent Density Augmentation around a Solute in Supercritical Solvent Bath: 1. A Mechanism Explanation and a New Phenomenon

A recently proposed partitioned density functional (DF) approximation (Phys. Rev. E 2003, 68, 061201) and an adjustable parameter-free version of a Lagrangian theorem-based DF approximation (LTDFA: Phys. Lett. A 2003, 319, 279) are combined to propose a DF approximation for nonuniform Lennard-Jones (LJ) fluid. Predictions of the present DF approximation for local LJ solvent density inhomogeneity around a large LJ solute particle or hard core Yukawa particle are in good agreement with existing simulation data. An extensive investigation about the effect of solvent bath temperature, solvent-solute interaction range, solvent-solute interaction magnitude, and solute size on the local solvent density inhomogeneity is carried out with the present DF approximation. It is found that a plateau of solvent accumulation number as a function of solvent bath bulk density is due to a coupling between the solvent-solute interaction and solvent correlation whose mathematical expression is a convolution integral appearing in the density profile equation of the DF theory formalism. The coupling becomes stronger as the increasing of the whole solvent-solute interaction strength, solute size relative to solvent size, and the closeness to the critical density and temperature of the solvent bath. When the attractive solvent-solute interaction becomes large enough and the bulk state moves close enough to the critical temperature of the solvent bath, the maximum solvent accumulation number as a function of solvent bath bulk density appears near the solvent bath critical density; the appearance of this maximum is in contrast with a conclusion drawn by a previous investigation based on an inhomogeneous version of Ornstein-Zernike integral equation carried out only for a smaller parameter space than that in the present paper. Advantage of the DFT approach over the integral equation is discussed.

Sedimentation Equilibrium of Colloidal Suspensions in a Planar Pore Based on Density Functional Theory and the Hard-Core Attractive Yukawa Model

The sedimentation equilibrium of colloidal suspensions modeled by hard-core attractive Yukawa (HCAY) fluids in a planar pore is studied. The density profile of the HCAY fluid in a gravitational field and its distribution between the pore and uniform phases are investigated by a density functional theory (DFT) approach, which results from employing a recently proposed parameter-free version of the Lagrangian theorem-based density functional approximation (Zhou, S. Phys. Lett. A 2003, 319, 279) for hard-sphere fluids to the hard-core part of the HCAY fluid, and the second-order functional perturbation expansion approximation to the tail part as was done in a recent partitioned density functional approximation (Zhou, S. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 061201). The resultant DFT approach is, thus, the first adjustable parameter-free DFT for HCAY fluids. The validity of the present DFT for HCAY fluids of reduced range parameter z(red) = 1.8 under various external potentials is established in the first of the papers cited previously. The present DFT for HCAY fluids can predict the radial distribution function for the bulk HCAY fluid accurately in the colloidal limit (large value of z(red)), and in the hard-sphere limit, its prediction for the density profile of the hard-sphere fluid in a gravitational field is in very good agreement with the existing simulation data. The dependence of the density profile and distribution coefficient on the magnitude of the interparticle attraction, gravitational field, and degree of confinement is investigated in detail by the present DFT approach. Intuitive and qualitative analyses are also compared with the quantitative DFT calculational results.

Universal calculational recipe for the calculation of solvent-mediated potential: (II) based on density functional theory

A universal recipe for the calculation of solvent-mediated potential (SMP) by a density functional (DF) approach is proposed. Parameter free version of a LTDFA is employed for the solvent hard core correlation and a BPGG bridge functional is modified for solute–solvent correlation. The resultant predictions for SMP and solvent-mediated force are in better agreement with simulation than that from a previous universal DF theory based on fundamental measure functional. Differences and relative merits of the present framework and a previous one compared with a potential distribution theory-based theory are discussed.

Application of Lagrangian theorem-based density-functional approximation free of adjustable parameters to nonhard-sphere fluid

A recently proposed parameter free version of a Lagrangian theorem-based density functional approximation (LTDFA) [S. Zhou, Phys. Lett. A 319, 279 (2003)] for hard-sphere fluid is applied to hard-core attractive Yukawa model fluid by dividing bulk second-order direct correlation function (DCF) of fluid under consideration into hard-core part and tail part. The former is treated by the parameter free version of the LTDFA, while the tail part is treated by second-order functional perturbation expansion approximation as done in a recent partitioned DFA [S. Zhou, Phys. Rev. E 68, 061201 (2003)]. Two versions of mean spherical approximation (MSA) for the bulk second-order DCF are employed as input, one is the less accurate plain MSA whose tail part of the second-order DCF is strictly independent of a density argument, the other is the more accurate inverse temperature expansion version of the MSA whose tail part is not strictly independent of the density argument. Calculational results indicate that prediction based on the plain MSA is far more accurate than that based on the inverse temperature expansion version of the MSA. The reason is considered to be that the partitioned DFA requires that the tail part is highly or completely independent of the density argument, the plain MSA, by assuming that the tail part is exactly the potential itself, embodies all of the nonlinearities into the hard-core part which can be treated satisfactorily by the parameter free version of the LTDFA. The present investigation results in a universal method for constructing DFA for nonuniform any nonhard-sphere interaction potential fluids.

Paradoxes in Double Extension Set Theories

Three systems of “double extension set theory” have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs.

FUSE Spectroscopy and Heavy Element Abundances in Hot, Hydrogen-Rich Subdwarfs

We have secured FUSE observations for a sample of hot, hydrogen-rich subdwarf B stars. The main objective of this project is to map in a more detailed way than has been done in the past pattern of heavy element abundances in sdB stars in order to understand the competing roles of gravitational settling, radiative element support, and mass loss in their photospheres. We present abundances analyses for a subsample of four objects and compare these results with predictions of the parameter-free version of the radiative levitation theory.