Arbitrary Pair Research Articles

A Pattern-Based SpGEMM Library for Multi-Core and Many-Core Architectures

General sparse matrix-matrix multiplication (SpGEMM) is one of the most important mathematical library routines in a number of applications. In recent years, several efficient SpGEMM algorithms have been proposed, however, most of them are based on the compressed sparse row (CSR) format, and the possible performance gain from exploiting other formats has not been well studied. And some specific algorithms are restricted to parameter tuning that has a significant impact on performance. So the particular format, algorithm, and parameter that yield the best performance for SpGEMM remain undetermined. In this article, we conduct a prospective study on format-specific parallel SpGEMM algorithms and analyze their pros and cons. We then propose a pattern-based SpGEMM library, that provides a unified programming interface in the CSR format, analyses the pattern of two input matrices, and automatically determines the best format, algorithm, and parameter for arbitrary matrix pairs. For this purpose, we build an algorithm set that integrates three new designed algorithms with existing popular libraries, and design a hybrid deep learning model called MatNet to quickly identify patterns of input matrices and accurately predict the best solution by using sparse features and density representations. The evaluation shows that this library consistently outperforms the state-of-the-art library. We also demonstrate its adaptability in an AMG solver and a BFS algorithm with 30 percent performance improvement.

Planning of Power Grasps Using Infinite Program Under Complementary Constraints

We propose an optimization-based approach to plan power grasps. Central to our method is a reformulation of grasp planning as an infinite program under complementary constraints (IPCC), which allows contacts to happen between arbitrary pairs of points on the object and the robot gripper. We show that IPCC can be reduced to a conventional finite-dimensional nonlinear program (NLP) using a kernel-integral relaxation. Moreover, the values and Jacobian matrices of the kernel-integral can be evaluated efficiently using a modified Fast Multipole Method (FMM). We further guarantee that the planned grasps are collision-free using primal barrier penalties. We demonstrate the effectiveness, robustness, and efficiency of our grasp planner on a row of challenging 3D objects and high-DOF grippers, such as Barrett Hand and Shadow Hand, where our method achieves superior grasp qualities over competitors.

INTERPRETING A FIELD IN ITS HEISENBERG GROUP

AbstractWe improve on and generalize a 1960 result of Maltsev. For a field F, we denote by $H(F)$ the Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in $H(F)$ , using existential formulas with an arbitrary non-commuting pair of elements as parameters. We show that F is interpreted in $H(F)$ using computable $\Sigma _1$ formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, Melnikov, R. Miller, and Montalbán. This proof allows the possibility that the elements of F are represented by tuples in $H(F)$ of no fixed arity. The second proof is direct, giving explicit finitary existential formulas that define the interpretation, with elements of F represented by triples in $H(F)$ . Looking at what was used to arrive at this parameter-free interpretation of F in $H(F)$ , we give general conditions sufficient to eliminate parameters from interpretations.

Optimal horizontal joinability on the Engel group

On the Engel group we solve the problem of finding the minimal number of segments of integral lines of left-invariant basis horizontal vector fields necessary for joining an arbitrary pair of points. We prove the best version of Rashevskii–Chow Theorem on Engel group.

Biological factors in the synthetic construction of overlapping genes

BackgroundOverlapping genes (OLGs) with long protein-coding overlapping sequences are disallowed by standard genome annotation programs, outside of viruses. Recently however they have been discovered in Archaea, diverse Bacteria, and Mammals. The biological factors underlying life’s ability to create overlapping genes require more study, and may have important applications in understanding evolution and in biotechnology. A previous study claimed that protein domains from viruses were much better suited to forming overlaps than those from other cellular organisms - in this study we assessed this claim, in order to discover what might underlie taxonomic differences in the creation of gene overlaps.ResultsAfter overlapping arbitrary Pfam domain pairs and evaluating them with Hidden Markov Models we find OLG construction to be much less constrained than expected. For instance, close to 10% of the constructed sequences cannot be distinguished from typical sequences in their protein family. Most are also indistinguishable from natural protein sequences regarding identity and secondary structure. Surprisingly, contrary to a previous study, virus domains were much less suitable for designing OLGs than bacterial or eukaryotic domains were. In general, the amount of amino acid change required to force a domain to overlap is approximately equal to the variation observed within a typical domain family. The resulting high similarity between natural sequences and those altered so as to overlap is mostly due to the combination of high redundancy in the genetic code and the evolutionary exchangeability of many amino acids.ConclusionsSynthetic overlapping genes which closely resemble natural gene sequences, as measured by HMM profiles, are remarkably easy to construct, and most arbitrary domain pairs can be altered so as to overlap while retaining high similarity to the original sequences. Future work however will need to assess important factors not considered such as intragenic interactions which affect protein folding. While the analysis here is not sufficient to guarantee functional folding proteins, further analysis of constructed OLGs will improve our understanding of the origin of these remarkable genetic elements across life and opens up exciting possibilities for synthetic biology.

The Lp-to-Lq boundedness of commutators with applications to the Jacobian operator

Supplying the missing necessary conditions, we complete the characterisation of the Lp→Lq boundedness of commutators [b,T] of pointwise multiplication and Calderón–Zygmund operators, for arbitrary pairs of 1<p,q<∞ and under minimal non-degeneracy hypotheses on T.For p≤q (and especially p=q), this extends a long line of results under more restrictive assumptions on T. In particular, we answer a recent question of Lerner, Ombrosi, and Rivera-Ríos by showing that b∈BMO is necessary for the Lp-boundedness of [b,T] for any non-zero homogeneous singular integral T. We also deal with iterated commutators and weighted spaces.For p>q, our results are new even for special classical operators with smooth kernels. As an application, we show that every f∈Lp(Rd) can be represented as a convergent series of normalised Jacobians Ju=det⁡∇u of u∈W˙1,dp(Rd)d. This extends, from p=1 to p>1, a result of Coifman, Lions, Meyer and Semmes about J:W˙1,d(Rd)d→H1(Rd), and supports a conjecture of Iwaniec about the solvability of the equation Ju=f∈Lp(Rd).

Power-optimal, stabilized entangling gate between trapped-ion qubits

To achieve scalable quantum computing, improving entangling-gate fidelity and its implementation efficiency are of utmost importance. We present here a linear method to construct provably power-optimal entangling gates on an arbitrary pair of qubits on a trapped-ion quantum computer. This method leverages simultaneous modulation of amplitude, frequency, and phase of the beams that illuminate the ions and, unlike the state of the art, does not require any search in the parameter space. The linear method is extensible, enabling stabilization against external parameter fluctuations to an arbitrary order at a cost linear in the order. We implement and demonstrate the power-optimal, stabilized gate on a trapped-ion quantum computer.

Evaluation of the union bound for the decoding error probability using characteristic functions

Introduction: Since the exact value of a decoding error probability cannot usually be calculated, an upper bounding technique is used. The standard approach for obtaining the upper bound on the maximum likelihood decoding error probability is based on the use of the union bound and the Chernoff bound, as well as its modifications. For many situations, this approach is not accurate enough. Purpose: Development of a method for exact calculation of the union bound for a decoding error probability, for a wide class of codes and memoryless channels. Methods: Use of characteristic functions of logarithm of the likelihood ratio for an arbitrary pair of codewords, trellis representation of codes and numerical integration. Results: The resulting exact union bound on the decoding error probability is based on a combination of the use of characteristic functions and the product of trellis diagrams for the code, which allows to obtain the final expression in an integral form convenient for numerical integration. An important feature of the proposed procedure is that it allows one to accurately calculate the union bound using an approach based on the use of transfer (generating) functions. With this approach, the edge labels in the product of trellis diagrams for the code are replaced by their corresponding characteristic functions. The final expression allows, using the standard methods of numerical integration, to calculate the values of the union bound on the decoding error probability with the required accuracy. Practical relevance: The results presented in this article make it possible to significantly improve the accuracy of the bound of the error decoding probability, and thereby increase the efficiency of technical solutions in the design of specific coding schemes for a wide class of communication channels.

A pre-existing self-referential anchor is not necessary for self-prioritisation

Self-prioritisation effect (SPE) has consistently occurred in perceptual matching tasks in which neutral stimuli are paired with familiar labels representing different identities (e.g., triangle-Self, square-Friend). Participants are faster and more accurate at judging self-related shape-label pairings than the pairings associated with others. Much evidence has suggested that the SPE is driven by the self acting as an integrative hub that enhances stimulus processing (e.g., triangle). However, there is a growing debate as to whether the SPE is genuine or determined by the labels (e.g., ‘me’, ‘you’) being pre-existing self-referential anchor points. We investigated this in an adapted perceptual matching task in which participants were instructed to associate arbitrary stimulus pairs (visual features: shape and colour) with different people and then immediately carried out a colour-shape matching task. The results showed the standard pattern of the SPE in this perceptual matching task without familiar labels, indicating that the effect is not critically dependent on familiar labels. Further analysis revealed that the SPE emerged only when the complete shape-colour pairing was presented rather than individual elements (self-shape or self-colour). The theoretical implications of these findings are considered.

Critical layer thickness of wurtzite heterostructures with arbitrary pairs of growth planes and slip systems

We establish a calculation method to determine the critical layer thickness of the lattice relaxation in wurtzite heterostructures with arbitrary pairs of growth planes and slip systems. The calculation, which is based on the force balance model, takes the friction force and thermal assistance for the dislocation motion into account. Experimentally, Al x Ga1 − x N/AlN heterostructures are fabricated. The established method well reproduces the crystallographic orientations of experimentally observed dislocation lines.

Tripartite entropic uncertainty relation under phase decoherence

We formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.

A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems

In this paper, we describe and establish iteration-complexity of two accelerated composite gradient (ACG) variants to solve a smooth nonconvex composite optimization problem whose objective function is the sum of a nonconvex differentiable function f with a Lipschitz continuous gradient and a simple nonsmooth closed convex function h. When f is convex, the first ACG variant reduces to the well-known FISTA for a specific choice of the input, and hence the first one can be viewed as a natural extension of the latter one to the nonconvex setting. The first variant requires an input pair (M, m) such that f is m-weakly convex, \(\nabla f\) is M-Lipschitz continuous, and \(m \le M\) (possibly \(m<M\)), which is usually hard to obtain or poorly estimated. The second variant on the other hand can start from an arbitrary input pair (M, m) of positive scalars and its complexity is shown to be not worse, and better in some cases, than that of the first variant for a large range of the input pairs. Finally, numerical results are provided to illustrate the efficiency of the two ACG variants.

On the complexity of implementation of a system of two monomials by composition circuits

Abstract The complexity of implementation of systems of monomials by composition circuits is studied. In such a model, the complexity is understood as the smallest number of composition operations required for computation of a system of monomials. The main result is an exact formula which, for an arbitrary pair of monomials, gives the complexity of their joint implementation by composition circuits.

Functional theory for Bose-Einstein condensates

One-particle reduced density matrix functional theory would potentially be the ideal approach for describing Bose-Einstein condensates. It namely replaces the macroscopically complex wavefunction by the simple one-particle reduced density matrix, therefore provides direct access to the degree of condensation and still recovers quantum correlations in an exact manner. We eventually initiate and establish this novel theory by deriving the respective universal functional $\mathcal{F}$ for general homogeneous Bose-Einstein condensates with arbitrary pair interaction. Most importantly, the successful derivation necessitates a particle-number conserving modification of Bogoliubov theory and a solution of the common phase dilemma of functional theories. We then illustrate this novel approach in several bosonic systems such as homogeneous Bose gases and the Bose-Hubbard model. Remarkably, the general form of $\mathcal{F}$ reveals the existence of a universal Bose-Einstein condensation force which provides an alternative and more fundamental explanation for quantum depletion.

Reliability assessment of stochastic networks with ER connectivity and ER dependency

In stochastic networks, nodes usually function dependently and interact with other nodes through connectivity links or dependency links. In this paper, the model for stochastic networks considering sub-networks with connectivity and dependency links of Erdös-Rényi (ER) topology is proposed, which is defined as networks with arbitrary pair of nodes randomly connected/depended by a constant probability. The reliability evaluation framework for the proposed networks is developed, where both of the extended multi-valued decision diagram (MDD) method and Monte Carlo simulation (MCS) are involved. The MDD method is proposed to assess the reliability of deterministic stochastic networks with ER connectivity and dependency, where arbitrary time to failure distributions of nodes are allowed. Based on the reliability evaluation for a stochastic network with a deterministic structure, the MCS is employed to achieve the reliability analysis of corresponding stochastic networks. Numerical examples are presented to demonstrate the proposed stochastic network model and reliability evaluation framework, where the probability distributions for the reliability of stochastic networks are provided.

Fundamental Limits of Lossless Data Compression With Side Information

The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions of the problem: Reference-based compression, when a single side information string is used repeatedly in compressing different source messages, and pair-based compression, where a different side information string is used for each source message. General achievability and converse theorems are established for arbitrary source-side information pairs. Nonasymptotic normal approximation expansions are proved for the optimal rate in both the reference-based and pair-based settings, for memoryless sources. These are stated in terms of explicit, finite-blocklength bounds, that are tight up to third-order terms. Extensions that go significantly beyond the class of memoryless sources are obtained. The relevant source dispersion is identified and its relationship with the conditional varentropy rate is established. Interestingly, the dispersion is different in reference-based and pair-based compression, and it is proved that the reference-based dispersion is in general smaller.

Mining Likely Analogical APIs Across Third-Party Libraries via Large-Scale Unsupervised API Semantics Embedding

Establishing API mappings between third-party libraries is a prerequisite step for library migration tasks. Manually establishing API mappings is tedious due to the large number of APIs to be examined. Having an automatic technique to create a database of likely API mappings can significantly ease the task. Unfortunately, existing techniques either adopt supervised learning mechanism that requires already-ported or functionality similar applications across major programming languages or platforms, which are difficult to come by for an arbitrary pair of third-party libraries, or cannot deal with lexical gap in the API descriptions of different libraries. To overcome these limitations, we present an unsupervised deep learning based approach to embed both API usage semantics and API description (name and document) semantics into vector space for inferring likely analogical API mappings between libraries. Based on deep learning models trained using tens of millions of API call sequences, method names and comments of 2.8 millions of methods from 135,127 GitHub projects, our approach significantly outperforms other deep learning or traditional information retrieval (IR) methods for inferring likely analogical APIs. We implement a proof-of-concept website ( https://similarapi.appspot.com ) which can recommend analogical APIs for 583,501 APIs of 111 pairs of analogical Java libraries with diverse functionalities. This scale of third-party analogical-API database has never been achieved before.

Studies of emission regions of the X-ray pulsar Hercules X-1 with pulse-phase-resolved spectra observed with Suzaku

Abstract Pulse-phase-resolved X-ray spectra of the X-ray pulsar Her X-1 observed with Suzaku are analyzed. The analysis is based on a hypothesis that the observed variations of the continuum spectra associated with the neutron star spin originate in the changes of the projection areas of the emission regions viewed from the observer, and that the spectral shape observed from each of the emission regions does not change with the viewing angle variation. We calculate the ratios of the fluxes in each energy bin between arbitrary pairs of the pulse-phase-resolved spectra over the entire energy range. We identify flat portions in these ratio spectra, which are likely to indicate the intrinsic emission components that have invariant spectral shapes, in the three energy bands of below ∼1 keV, 2–6 keV, and above ∼18 keV. Then, we approximately solve the simultaneous equations for the intrinsic spectral components from a pair of the phase-resolved spectra that show flat portions in the ratio spectrum. As a result, spectra of the three components are obtained as the low-, medium-, and high-energy bands corresponding to those for the flat portions. They are found to be well fitted with a soft blackbody, a cut-off power law, and a hard blackbody model, respectively. Finally, we fit all the phase-resolved spectra simultaneously with a composite model of three continuum components together with a cyclotron absorption feature and an iron line, and obtain an acceptable result. The origins of the cut-off power-law and hard blackbody components are discussed in relation to recently developed theoretical models.

Full-Stokes Polarization Perfect Absorption with Diatomic Metasurfaces.

Metamaterial-based perfect absorbers provide efficient ways for selective absorption of light with both linear or circular polarizations. Perfect absorption for an arbitrary polarization requires the development of subwavelength structures absorbing efficiently elliptically polarized light, but they remain largely unexplored. Here, we design and realize experimentally novel plasmonic metasurfaces for full-Stokes polarization perfect absorption in the mid-infrared. The metasurface unit cell consists of coupled anisotropic meta-atoms forming a diatomic metamolecule. The designed plasmonic metastructures provide a strong field enhancement by at least 1 order of magnitude higher than conventional perfect absorbers. In experiment, our plasmonic metasurfaces demonstrate sharp differentiation of spectral responses for an arbitrary pair of orthogonal polarization states (linear, circular, or elliptical) providing perfect absorption for one polarization with strong reflection for its counterpart. Our results suggest a novel route for efficient control of light polarization in metasurfaces offering numerous potential applications ranging from thermal imaging to chiral molecule detection.

Wideband OFDM-Based Communications in Bus Topology as a Key Enabler for Industry 4.0 Networks

The Industry 4.0 paradigm conceives a cyber-physical supporting framework for the manufacturing processes in smart factories. In this context, solutions concerning the wired communications at the field-level have been reported which utilize either fieldbuses, which exhibit a huge distance range but a reduced data rate in a bus topology, or Ethernet-based technologies, which provide an increased data rate but reduced distance in a ring topology. To overcome this shortage, we propose the use of orthogonal frequency division multiplexing (OFDM) to significantly increase the achievable data rates over large distances in industrial bus systems. Also, we establish a novel methodology to compute the signal-to-noise ratio between arbitrary pairs of nodes, which in turn allows to compute the communication capacity. Our wideband system was validated by connecting up to 32 nodes in the distance range 100 m–1 km. Compared to fieldbuses, the results of the proposal exhibit an amazing improvement in data rate of about fifty times for 100m distance and more than ten times for 0.5 km. Moreover, with respect to Ethernet-based solutions, the results show a relevant improvement in the data rate of around five times for 100m distance, but Ethernet-based systems cannot go beyond this distance, to which our proposal is not limited.