General Number Research Articles

When one is singular: Notes on zero-person constructions in Latvian

Axel Holvoet has demonstrated that Latvian has two types of zero-person constructions which formally differ in grammatical number, and that the singular type has a parallel in Finnic, but not in Lithuanian. This paper shows that the meanings covered by the two types are distinct and do not overlap. Using the framework proposed by Gast and van der Auwera for the description of human impersonal pronouns, it is shown that the singular type is characterized by non-veridicality and an internal perspective. As in Finnish, but not Estonian, it is used in conditional sentences with all kinds of verbs. The plural type is used in Latvian as well as in Lithuanian with veridical propositions and an external perspective.

Logarithmic submajorizations inequalities for operators in a finite von Neumann algebra

The aim of this paper is to study the logarithmic submajorizations inequalities for operators in a finite von Neumann algebra. Firstly, some logarithmic submajorizations inequalities due to Garg and Aulja are extended to the case of operators in a finite von Neumann algebra. As an application, we get some new Fuglede-Kadison determinant inequalities of operators in that circumstance. Secondly, we improve and generalize to the setting of finite von Neumann algebras, a generalized Hölder type generalized singular numbers inequality.

Predicting the duration of chaotic transients in excitable media

The spatiotemporal dynamics of excitable media may exhibit chaotic transients. We investigate this transient chaos in the 2D Fenton–Karma model describing the propagation of electrical excitation waves in cardiac tissue and compute the average duration of chaotic transients in dependence on model parameter values. Furthermore, other characteristics like the dominant frequency, the size of the excitable gap, pseudo ECGs, the number of phase singularities and parameters characterizing the action potential duration restitution curve are determined and it is shown that these quantities can be used to predict the average transient time using polynomial regression.

Reassessing gender in Ogbe-Oloma

Abstract We re-assess the gender system of Ogbe-Oloma, an Edoid village variety of Nigeria. System exponents are prefixes that define form class and reflect grammatical number. We find that eight agreement classes undergird fourteen genders, while seventeen nominal form classes frame twenty-five number inflections. Prefix mapping from inflection to gender is non-isomorphic. Mapping is however constrained by syllable shape, CV- versus V-, and alliterative sound quality of prefix consonant, not vowel. In addition, several number inflections trigger agreement in multiple genders leading to one gender that exclusively refers to nouns with human reference.

Dependent plurals and three levels of multiplicity

The paper focuses on the semantics of distributivity, grammatical number, and cardinality predicates (numerals and modifiers like several). I argue that constructions involving so-called ‘dependent plurals’, i.e. plurals lacking cardinality predicates occurring in the scope of certain quantificational items such as all and most (e.g. All the girls were wearing hats), pose a challenge to familiar semantic frameworks that distinguish between two sources of multiplicity: mereological plurality and distributive quantification. I argue that dependent plural readings should be analysed as distinct both from cumulative readings and distributive readings, in the classical sense. I demonstrate how this can be accomplished in a semantic framework where expressions are evaluated relative to sets of assignments, or plural info states (van den Berg, in Stokhof and Torenvliet (eds) Proceedings of the 7th Amsterdam Colloquium, ILLC, University of Amsterdam, Amsterdam, 1990, in Dekker and Stokhof (eds) Proceedings of the 9th Amsterdam Colloquium, ILLC, University of Amsterdam, Amsterdam, 1994, Some aspects of the Internal Structure of Discourse. The Dynamics of Nominal Anaphora. PhD thesis, University of Amsterdam, 1996). The specific formal implementation is based on a modified version of Brasoveanu’s (Structured nominal and modal reference. PhD thesis, Rutgers, The State University of New Jersey, 2007, Linguist Philos 31(2):129–209. https://doi.org/10.1007/s10988-008-9035-0, 2008) Plural Compositional DRT. In this framework we are able to distinguish between two types of distributivity: weak distributivity across the assignments in a single plural info state and strong distributivity across multiple info states. I argue that both of these types of distributivity play a role in the semantics of natural language, accounting for the contrasting properties of ‘singular quantifiers’, such as each and every, and ‘plural quantifiers’, such as all and most. The contrasting properties of bare plurals and plurals involving cardinality modifiers are analysed in terms of the distinction between state-level and assignment-level (mereological) plurality.

Exotic image formation in strong gravitational lensing by clusters of galaxies – II. Uncertainties

ABSTRACT Due to the finite amount of observational data, the best-fitting parameters corresponding to the reconstructed cluster mass have uncertainties. In turn, these uncertainties affect the inferences made from these mass models. Following our earlier work, we have studied the effect of such uncertainties on the singularity maps in simulated and actual galaxy clusters. The mass models for both simulated and real clusters have been constructed using grale. The final best-fitting mass models created using grale give the simplest singularity maps and a lower limit on the number of point singularities that a lens has to offer. The simple nature of these singularity maps also puts a lower limit on the number of three image (tangential and radial) arcs that a cluster lens has. Hence, we estimate the number of galaxy sources giving rise to the three image arcs, which can be observed with the James Webb Space Telescope (JWST). We find that we expect to observe at least 20–30 tangential and 5–10 radial three-image arcs in the Hubble Frontier Fields cluster lenses with the JWST.

The interpretation of plural mass nouns in Greek

This paper focuses on the interpretation of what has been considered an expletive marker in the grammar of the Greek nominal domain: the plural number of mass nouns. We present the results of an experimental investigation on the interpretation of plural mass nouns by native speakers of this language, and we propose a speech act analysis according to which at the time of producing utterances that contain plural mass nouns the speaker performs two speech acts: an assertion and an expressive speech act by which (s)he publicly commits to an emotive stance of dislike towards the expressed proposition φ. This stance is analyzed as an emotive judgment with respect to φ, the expression of which directly transfers the speaker's emotion from the conversation into the speaker and addressee's common ground.

Singular numbers, entangled qubits transmission through a turbulent atmosphere and teleportation

Singular numbers, entangled qubits transmission through a turbulent atmosphere and teleportation

Influence of Fibrosis Amount and Patterns on Ventricular Arrhythmogenesis and Pumping Efficacy: Computational Study.

Myocardial fibrosis is an integral component of most forms of heart failure. Clinical and computational studies have reported that spatial fibrosis pattern and fibrosis amount play a significant role in ventricular arrhythmogenicity. This study investigated the effect of the spatial distribution of fibrosis and fibrosis amount on the electrophysiology and mechanical performance of the human ventricles. Seventy-five fibrosis distributions comprising diffuse, patchy, and compact fibrosis types that contain 10–50% fibrosis amount were generated. The spatial fibrosis distribution was quantified using the fibrosis entropy (FE) metric. Electrical simulations under reentry conditions induced using the S1–S2 protocol were conducted to investigate the fibrosis arrhythmogenicity. We also performed mechanical simulations to examine the influence of the fibrosis amount and the spatial distribution of fibrosis on the pumping efficacy of the LV. We observed that the mean FE of the compact type is the largest among the three types. The electrical simulation results revealed that the ventricular arrhythmogenicity of diffuse fibrosis depends on the fibrosis amount and marginally on the spatial distribution of fibrosis. Meanwhile, the ventricular arrhythmogenicity of the compact and patchy fibrosis pattern is more reliant on the spatial distribution of fibrosis than on the fibrosis amount. The average number of phase singularities (PSs) in the compact fibrosis pattern was the highest among the three patterns of fibrosis. The diffuse type of fibrosis has the lowest average number of PSs than that in the patchy and compact fibrosis. The reduction in the stroke volume (SV) showed high influence from the electrical instabilities induced by the fibrosis amount and pattern. The compact fibrosis exhibited the lowest SV among the three patterns except in the 40% fibrosis amount. In conclusion, the fibrosis pattern is as crucial as the fibrosis amount for sustaining and aggravating ventricular arrhythmogenesis.

Propagation-invariant laser beams with an array of phase singularities

In this work, we investigate multivortex beams with an infinite topological charge. Such optical vortices contain an array of an infinite, but countable, number of phase singularities (isolated intensity nulls), which typically have the unitary topological charge and are located either uniformly (or not uniformly) on a straight line (or on several crossing straight lines) in the beam transverse cross section. Such optical vortices are form invariant and their transverse intensity distribution is conserved on propagation, changing only in scale and rotation. The orbital angular momentum of such optical vortices is finite, since only a finite number of screw dislocations is located within the area of the notable intensity of the Gaussian beam, while the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to a parabolic growth of the orbital angular momentum of such beams.

The Use of Literature in the Foreign Language Classroom

The present study focuses on the use of literary texts in teaching Arabic and English as foreign languages. It is part of an action research project that also includes the design of a literature-based syllabus for teaching foreign language skills at the Department of Foreign Languages, University of the Western Cape, South Africa. The project deals also with piloting the materials and investigating the attitudes of the learners towards them. In particular, this study investigates the use of short stories and poems in the foreign language classroom. It shows how Oscar Wilde’s The Selfish Giant can be effectively used for teaching some syntactic constructions such as exclamation sentences. The study also explores the use of Shawqi’s al-thaʿlab wa al-dīk (i.e. The Fox and the Roaster) in teaching vocabulary and grammatical number in Arabic. Finally, the study uses Bahjat’s Ghurāb ʾibnaī ʾādam (i.e. The Crow of the Two Sons of Adam) to teach language skills and to introduce some multimodal activities such as adaptation and digital storytelling. The study has concluded that literature in general and short stories and poems in particular provide the learners with motivating resources that can assist them to develop their language skills and enhance their communicative and interpretive competence.

Mechanism of angiotensin receptor-neprilysin inhibitor in suppression of ventricular arrhythmia

BackgroundThe mechanisms underlying angiotensin receptor-neprilysin inhibitor (ARNi) suppression of ventricular arrhythmia (VA) are unclear. This study aimed to investigate the mechanism of ARNi-related suppression of VA in a heart failure (HF) model. MethodsNew Zealand white rabbits (n = 6 per group) were assigned to normal, HF [4 weeks of left ascending artery (LAD) ligation], angiotensin receptor blocker (ARB, valsartan at 27 mg/kg/day for 3 weeks after 1 week of LAD ligation), and ARNi (sacubitril at 34 mg/kg/day and valsartan at 27 mg/kg/day for 3 weeks after 1 week of LAD ligation) groups. Experiments involving echocardiogram, optical mapping, histological of trichrome stain and immunostain, and flow cytometry were performed. ResultsHF group had larger left ventricular (LV) internal dimensions in diastole and systole, and lower LV ejection fraction and fractional shortening than normal, ARB, and ARNi groups. HF group had a prolonged action potential duration (APD) and decreased conduction velocity (CV), which was mitigated in ARB and ARNi groups. HF group had a prolonged QRS duration, QT and QTc intervals, which was reversed in ARB and ARNi groups. HF group had a steeper maximum slope of APD restitutions, which was attenuated in normal, ARB, and ARNi groups. HF group had increased number of phase singularities (PSs) and VA inducibility than normal, ARB, and ARNi groups. A higher content of fibrosis was found in HF group than that in normal, ARB, and ARNi groups. Compared to ARB group, ARNi had a lower context of fibrosis. HF group had more peripheral blood CD4+ and CD8+ cells count than normal, ARB, and ARNi group. ConclusionsIn a rabbit model of ischemic HF, ventricular arrhythmogenesis could be suppressed by ARNi treatment. This appears to be mediated by reversing changes in the APD, CV, maximum slope of the APDR, PSs, fibrosis, and inflammation.

Structure and Topology Analysis of Separated Vortex in Forward-Swept Blade

Flow separation commonly affects the stability of turbomachines, especially under low-flowrate conditions. Compared with conventional blades, a forward-swept blade is more efficient at high flowrates. However, experiments and numerical simulations show that a forward-swept blade produces an unstable region under low flowrate. In this paper, the topological analysis is used to analyze the structure and size of flow separation in forward swept blades. Three-dimensional structure and formation mechanism of vortices in forward-swept blades are analyzed using the cross-section flow pattern method. For forward-swept blades, flow separation mainly occurs at the blade tip and corner, accompanied by clear velocity fluctuations, the break-up of shed vortices, and diffusion. With decreasing flowrate, the shedding vortices move forward and the speed of vortex annihilation gradually decreases. In addition, the number of singularities in the rotor passage increases with the decrease of flow rate, and the region affected by shedding vortex increases. The rotating direction of internal vortex in turbomachinery is fixed. The pressure surface, passage vortex, and concentrated shedding vortex were found to rotate clockwise, whereas the suction surface, corner vortex, and shedding vortex rotate in a counterclockwise direction.

Supplemental Material for “Where Are the . . . Fixations?”: Grammatical Number Cues Guide Anticipatory Fixations to Upcoming Referents and Reduce Lexical Competition

Supplemental Material for “Where Are the . . . Fixations?”: Grammatical Number Cues Guide Anticipatory Fixations to Upcoming Referents and Reduce Lexical Competition

Controllable manipulation of composite multi-singularity vortex array

This study proposes a composite optical vortex array with multiple singularities and controllable radius, phase, sign, and intensity based on the coaxial interference of Bessel–Gaussian​ (BG) beams. Different from the general petal-like beam, we destroy the symmetry of the composite vortex by changing the order of the Bessel function, resulting in the occurrence of positive and negative alternating unit vortex chains in the interference region. The rule of the influence of the topological charges (TCs) and the order of Bessel function on the locations and number of singularities is systematically investigated. Additionally, due to the effect of Gouy phase shift, the coaxial interference characteristics of non-diffractive BG beams with spatial mismatch are examined numerically using a split-step Fourier transform algorithm. The multi-singularity technology demonstrated in this study facilitates the control of complex particles and large-capacity optical communication; furthermore, it is of substantial significance for optical tweezers and optical imaging applications.

Quadrilateral multiblock decomposition via auxiliary subdivision

Abstract Automatic quadrilateral (quad) or hexahedral (hex) multiblock decomposition has been a topic of research for many years. The key challenges are to automatically determine where to place mesh singularities and how to generate a decomposition based on the mesh singularities to get the desired mesh orientation and distribution. In this work, a new idea of achieving these is proposed based on an auxiliary subdivision of the domain into smaller subdomains, followed by applying an equation, which calculates the net number of mesh singularities of a surface, to locate the quad mesh singularities. Under this idea, two different methods are presented based on the medial axis and the inward boundary offset. Both methods are conformal to the vertex classifications of the original domain, which guarantees a good mesh quality at the boundary. The mesh results are compared with a paving method and a cross-field method.

Effects of a quark chemical potential on the analytic structure of the gluon propagator

We perform complex analyses of the gluon propagator at nonzero quark chemical potential in the long-wavelength limit, using an effective model with a gluon mass term of the Landau-gauge Yang-Mills theory, which is a Landau-gauge limit of the Curci-Ferrari model with quantum corrections being included within the one-loop level. We mainly investigate complex poles of the gluon propagator, which could be relevant to confinement. Around typical values of the model parameters, we show that the gluon propagator has one or two pairs of complex conjugate poles depending on the value of the chemical potential. In addition to a pair similar to that in the case of zero chemical potential, a new pair appears near the real axis when the chemical potential is roughly between the effective quark mass and the effective gluon mass of the model. We discuss possible interpretations of these poles. Additionally, we prove the uniqueness of analytic continuation of the Matsubara propagator to a class of functions that vanish at infinity and are holomorphic except for a finite number of complex poles and singularities on the real axis.

Mechanisms for handling nested dependencies in neural-network language models and humans

Recursive processing in sentence comprehension is considered a hallmark of human linguistic abilities. However, its underlying neural mechanisms remain largely unknown. We studied whether a modern artificial neural network trained with “deep learning” methods mimics a central aspect of human sentence processing, namely the storing of grammatical number and gender information in working memory and its use in long-distance agreement (e.g., capturing the correct number agreement between subject and verb when they are separated by other phrases). Although the network, a recurrent architecture with Long Short-Term Memory units, was solely trained to predict the next word in a large corpus, analysis showed the emergence of a very sparse set of specialized units that successfully handled local and long-distance syntactic agreement for grammatical number. However, the simulations also showed that this mechanism does not support full recursion and fails with some long-range embedded dependencies. We tested the model's predictions in a behavioral experiment where humans detected violations in number agreement in sentences with systematic variations in the singular/plural status of multiple nouns, with or without embedding. Human and model error patterns were remarkably similar, showing that the model echoes various effects observed in human data. However, a key difference was that, with embedded long-range dependencies, humans remained above chance level, while the model's systematic errors brought it below chance. Overall, our study shows that exploring the ways in which modern artificial neural networks process sentences leads to precise and testable hypotheses about human linguistic performance.

On Young-type inequalities of measurable operators

Let be a semi-finite von Neumann algebra, be the set of all τ-measurable operators and be the generalized singular number of . We proved that if , and , then the Young-type inequality , for all t>0 holds.

Offshore crane non-linear stochastic response: novel design and extreme response by a path integration

ABSTRACT In this paper, the novel pendulum tuned mass damper model has been suggested as a potential practical engineering modification to an existing offshore crane setup. A number of potential numerical singularities have been circumvented and substantial numerical model accuracy has been reached. Main application of this study would be extreme value statistics, in case of e.g. extreme weather conditions causing collision between vessel and payload. Next, extreme statistics of random vibrations has been studied in this paper for a suggested pendulum tuned mass damper model under white noise excitation. Restoring force has been modelled as the elastic non-linear, and numerical comparison has been performed with the linearised restoring force model case to see the force non-linearity effect on the vessel payload response statistics. The statistics of non-linear case has been studied by applying the path integration method, based on the Markov property of the coupled dynamic system.