Null Operator Research Articles

Proleptic objects as complex-NPs

Abstract Proleptic (or prothetic) objects (Majaliwa remembered about Samson that he’s sick) present a particular puzzle because they appear to instantiate an unconstrained cross-clausal dependency between the proleptic object (Samson) and a correlate (he). The current analytical approach to prolepsis is relies on a syntactic mechanism of treating the embedded clause as a predicate, derived by merging a null operator which unselectively binds the correlate. This approach faces a number of known empirical challenges. Moreover, this work does not meaningfully engage with any of the recent semantic innovations in our understanding of embedded clauses (Kratzer 2006. Decomposing attitude verbs. Available at: http://semanticsarchive.net/Archive/DcwY2JkM/attitude-verbs2006.pdf). I offer an alternative to the CP-predicate approach, adopting three (semi-)independently motivated ideas concerning (i) the syntax of cross-clausal dependencies in Lohninger et al. (2022. From prolepsis to hyperraising. Philosophies 7(32)), (ii) the semantics of embedded clauses in Kratzer (2006. Decomposing attitude verbs. Available at: http://semanticsarchive.net/Archive/DcwY2JkM/attitude-verbs2006.pdf)/Moulton (2009. Not moving clauses: Connectivity in clausal arguments. Syntax 16(3). 250–291), and (iii) the semantics of about in Rawlins (2013. About about. Proceedings of SALT 23. 336–357)/Onea and Mardale (2020. From topic to object, grammaticalization differential object marking in Romanian. Canadian Journal of Linguistics/Revue Canadienne de Linguistique 65(3). 350–392). I argue that proleptic objects are complex-NPs, roughly, the thing about Samson. The somewhat particular properties of prolepsis are natural consequences of these combined ideas. I further present empirical evidence from Japanese that the complex-NP analysis is on the right track. This analysis deepens our understanding of prolepsis by including both semantic and syntactic factors.

Light-ray sum rules and the c-anomaly

In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly ∆a has been related to the average null energy. We extend this result to derive a sum rule for the other anomaly coefficient, ∆c, in terms of the stress tensor three-point function. While the sum rule for ∆a is an expectation value of the averaged null energy operator, and therefore positive, the result for ∆c involves the off-diagonal matrix elements, so it does not have a fixed sign.

Topological equivalence of nonhyperbolic nonautonomous systems

Backes, Dragičević and Palmer proved in [1, J. Differential Equations 2021] a C0 linearization result for nonautonomous coupled systems, whose linear part is nonhyperbolic but the second subsystem in their equations remains unchanged. In this paper, we establish a topological equivalence sending the solutions of the semilinear evolution equationx′=A(t)x+f(t,x,y),y′=r(t,x,y), onto those of its nonhyperbolic linearized partx′=A(t)x,y′=0. We require that one of the linear subsystem x′=A(t)x admits a nonuniform strong exponential dichotomy, but the other is a critical case, i.e., its linear part is a null operator. Then the difficulty arises: how to implement the linearization of the second subsystem? We will overcome the difficulty by introducing an implicit function, which enable us to construct equivalent functions to achieve the topological conjugacy between nonhyperbolic systems.

On the set of supercyclic operators

AbstractIn this article, we address a problem posed by Bayart regarding the existence of an infinite‐dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We fully resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on contains, up to the null operator, an isometric copy of .

A Minimalist Account of Free Relative Clauses in Zahrani Spoken Arabic

This paper explores the syntax of free relative clauses in Zahrani Spoken Arabic (henceforth ZSA). The paper shows that ZSA possesses two types of free relative clauses, viz., nominal free relative clauses and adverbial free relative clauses. The focus of the paper is on nominal free relative clauses. It is shown that nominal free relative clauses can appear in a subject position and a direct object position, and the range of relativization involves subject, direct object, indirect object, prepositional object and possessor relativization. The derivation of free relatives in ZSA involves resumption relativization strategy only where gaps are treated as null resumptive pronouns. As for distribution of null and overt resumptive clitics, there is an alternation between the use of null and overt resumptive pronouns/clitics in subject and direct object position. However, the utilization of overt resumptive pronouns/clitics is mandatory in indirect object, prepositional object and possessor position. It is argued that the free relative markers illi: and mi:n are complementizers. Furthermore, as null and overt resumptive clitics exhibit a big resemblance with respect to their behaviour in the coordinate structures and parasitic gaps, both free relatives with null or resumptive pronouns/clitics involve a null operator movement (in non-island contexts) from inside the free relative clause to the specifier of a complementizer phrase (spec CP). The CP is adjoined to a null antecedent occupying the head of a noun phrase (NP) which is a complement of a determiner phrase (DP) with an empty D.

Model-Based Simultaneous Multi-Slice (SMS) Reconstruction with Hankel Subspace Learning for Accelerated MR T1 Mapping

Herein, we propose a novel model-based simultaneous multi-slice (SMS) reconstruction method by exploiting data-driven parameter modeling for highly accelerated T1 parameter quantification. We assume that the predefined slice-specific null space operator remains invariant along the parameter dimension. We incorporate the parameter dimension into SMS-HSL to exploit Hankel-structured and Casorati matrices. Given this consideration, the SMS signal is reformulated in k-p space as a constrained optimization problem that exploits rank deficiency for the Hankel-structured matrix and a finite-dimensional basis for a subspace containing slowly evolving signals in the parameter direction. The proposed model-based SMS reconstruction method is validated on in vivo data and compared with state-of-the-art methods with slice acceleration factors of 3 and 5, including an in-plane acceleration factor of 2. The experimental results demonstrate that the proposed method performs effective slice unfolding and signal recovery in reconstructed images and T1 maps with high precision as compared to the state-of-the-art methods.

The interaction of idioms and aspect in Polish

AbstractThis study contributes to a longstanding discussion on the status of aspectual morphology and the aspectual architecture in Slavic by investigating aspectual properties of perfective and imperfective VP idioms in Polish. The investigation reveals that only lexical prefixes which can result in idiosyncratic meanings are part of basic perfective VP idioms. Building on the idea that little v is a demarcation line for idiomatic meanings, it is concluded that lexical prefixes are vP-internal. It is also shown that basic imperfective VP idioms are compatible with some superlexical prefixes and basic perfective VP idioms are compatible with secondary imperfective morphology, which suggests that such morphology is vP-external. Further semantic analysis of the interaction of basic imperfective VP idioms with different classes of superlexical prefixes shows that the compatible ones measure over some scale associated with vP-external material or the temporal trace of an (idiomatic) event. In contrast, the incompatible ones measure over a scale encoded by a verbal predicate or impose semantic restrictions on its argument and hence they intervene in the semantics of a VP idiom. Based on stacking facts and the interaction of different classes of superlexical prefixes with secondary imperfective morphology, two classes of superlexical prefixes are distinguished: high (projected above secondary imperfective) and low (projected below it). These observations are compatible with the view that aspectual morphology is separated from PFV and IPFV operators. The former may merge lower in the hierarchy, and the latter act at the level of AspP as phonologically null operators.

Parallel imaging reconstruction using spatial nulling maps.

To develop a robust parallel imaging reconstruction method using spatial nulling maps (SNMs). Parallel reconstruction using null operations (PRUNO) is a k-space reconstruction method where a k-space nulling system is derived using null-subspace bases of the calibration matrix. ESPIRiT reconstruction extends the PRUNO subspace concept by exploiting the linear relationship between signal-subspace bases and spatial coil sensitivity characteristics, yielding a hybrid-domain approach. Yet it requires empirical eigenvalue thresholding to mask the coil sensitivity information and is sensitive to signal- and null-subspace division. In this study, we combine the concepts of null-subspace PRUNO and hybrid-domain ESPIRiT to provide a more robust reconstruction method that extracts null-subspace bases of calibration matrix to calculate image-domain SNMs. Multi-channel images are reconstructed by solving an image-domain nulling system formed by SNMs that contain both coil sensitivity and finite image support information, therefore, circumventing the masking-related procedure. The proposed method was evaluated with multi-channel 2D brain and knee data and compared to ESPIRiT. The proposed hybrid-domain method produced quality reconstruction highly comparable to ESPIRiT with optimal manual masking. It involved no masking-related manual procedure and was tolerant of the actual division of null- and signal-subspace. Spatial regularization could be also readily incorporated to reduce noise amplification as in ESPIRiT. We provide an efficient hybrid-domain reconstruction method using multi-channel SNMs that are calculated from coil calibration data. It eliminates the need for coil sensitivity masking and is relatively insensitive to subspace separation, therefore, presenting a robust parallel imaging reconstruction procedure in practice.

Wormholes, geons, and the illusion of the tensor product

In this paper I argue that the Hilbert space of states of a holographic, traversable wormhole does not factorize into the tensor product of the boundary Hilbert spaces. After presenting the general argument I analyze two examples: the scalar sectors of the BTZ geon and the AdS2 eternal wormhole. Utilizing real-time holography I derive the Hilbert spaces, identify the dual states and evaluate correlation functions. I show that the number of peculiarities associated with the wormhole and black hole physics emerges once the factorization is a priori assumed. This includes null states and null operators, highly entangled vacuum states and the cross-boundary interactions all emerging as avatars of non-factorization.

FAT: An In-Memory Accelerator With Fast Addition for Ternary Weight Neural Networks

Convolutional neural networks (CNNs) demonstrate excellent performance in various applications but have high computational complexity. Quantization is applied to reduce the latency and storage cost of CNNs. Among the quantization methods, binary and ternary weight networks (BWNs and TWNs) have a unique advantage over 8 and 4-bit quantization. They replace the multiplication operations in CNNs with additions, which are favored on in-memory-computing (IMC) devices. IMC acceleration for BWNs has been widely studied. However, though TWNs have higher accuracy and better sparsity than BWNs, IMC acceleration for TWNs has limited research. TWNs on the existing IMC devices are inefficient because the sparsity is not well utilized, and the addition operation is not efficient. In this article, we propose FAT as a novel IMC accelerator for TWNs. First, we propose a sparse addition control unit, which utilizes the sparsity of TWNs to skip the null operations on zero weights. Second, we propose a fast addition scheme based on the memory sense amplifier (SA) to avoid the time overhead of both carry propagation and writing back the carry to memory cells. Third, we further propose a combined-stationary data mapping to reduce the data movement of activations and weights and increase the parallelism across memory columns. Simulation results show that for addition operations at the SA level, FAT achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.00\times $ </tex-math></inline-formula> speedup, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.22\times $ </tex-math></inline-formula> power efficiency, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.22\times $ </tex-math></inline-formula> area efficiency compared with a state-of-the-art IMC accelerator ParaPIM. FAT achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10.02\times $ </tex-math></inline-formula> speedup and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$12.19\times $ </tex-math></inline-formula> energy efficiency compared with ParaPIM on networks with 80% average sparsity.

Generalized self-calibrating simultaneous multi-slice MR image reconstruction from 3D Fourier encoding perspective.

This work introduces a novel, k-space based one-step solution for simultaneous multi-slice MR image reconstruction from 3D Fourier encoding perspective. With undersampled SMS imaging, image reconstruction suffers from both inter-slice leakages and in-plane aliasing artifacts. Aliasing separation becomes further challenging in the presence of discrepancies between calibration and imaging. To address them, in this work a measured SMS 3D k-space with additional calibrating signals is decomposed into SMS imaging and self-calibrating data sets. Extended controlled aliasing is performed by upsampling the measured data in the kz-direction. A slice-specific null space operator is then learned using extended self-calibration exploiting target slices and additional in-plane-shifted images. Inter-slice leakages and in-plane aliasing artifacts are jointly resolved in a single step by solving a constrained optimization problem in which null space reconstruction consistency is balanced with a Hankel-structured low rank prior while data fidelity in 3D Fourier space is enforced. Retrospective and prospective studies are performed to validate the effectiveness of the proposed method in various regions including knee and L-spine.

A Highly Efficient Si-/SiC-Based Hybrid Active NPC Converter With a Novel Modulation Scheme

With the increasing demand for high-performance power electronic systems, the semiconductor device utilization has gained significant importance. This article proposes the Si/SiC devices based active neutral-point-clamped converter comprising SiC-based H-bridge structure. A novel pulsewidth modulation (PWM) scheme is also proposed that results in an effective utilization of the switching devices. In the proposed converter, the Si devices are soft-switched for all power-factor loading conditions. Therefore, high efficiency can be obtained even at high switching frequency operation with wide range of power factor values. Further, the conduction losses of the SiC <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mosfet</small> s are minimized by strategically selecting the switching states in such a way that the SiC <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mosfet</small> s conduct in parallel conduction paths during the null state operation. This leads to further enhanced efficiency. This article presents the detailed operating principle of the proposed topology operated with the presented PWM scheme. Moreover, a device loss analysis is presented to evaluate the conduction and switching losses of the proposed topology. The presented experimental results validate the performance parameters of the proposed topology with the proposed PWM scheme. Finally, the proposed PWM scheme is compared with the existing PWM schemes using efficiency values of the proposed and some of the prominent existing converter configurations.

Entropy variations and light ray operators from replica defects

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d − 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

Keep only strong

While Horn (1969) proposed that [[only]](p) presupposes that the prejacent p is true, von Fintel &amp; Iatridou (2007) showed that the expected prejacent inference is not observed when a necessity modal occurs in the scope of only: [[only]](□p) may convey that p is possible, rather than necessary. What is the mechanism behind the surprisingly weak inference? The approach in von Fintel &amp; Iatridou 2007 is to revise the analysis of only itself to weaken its contribution. In this paper, however, we argue that Horn’s only is correct after all, and introduce a source of weakening separate from only. In particular, in von Fintel &amp; Iatridou’s modal environment, a phonetically null operator (AT LEAST; Crnic̆ 2011, Schwarz 2005) occurs in the scope of only to weaken the presupposed prejacent. Much recent attention has been paid to covert operators which strengthen meaning, in particular a covert EXH with a meaning similar to only (e.g. Chierchia 2006, Fox 2007, Chierchia et al. 2012). A key consequence of our analysis is that natural language incorporates a covert weakening operator, as well. EARLY ACCESS

Transverse spin in the light-ray OPE

We study a product of null-integrated local operators {mathcal{O}}_1 and {mathcal{O}}_2 on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious d − 2 dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin J1 + J2− 1. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins J1 + J2− 1 + n, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin 3 (as described by Hofman and Maldacena), but also novel terms with spin 5, 7, 9, etc. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in mathcal{N} = 4 SYM, finding perfect agreement.

Spaceability of sets of p-compact maps

We provide quite sufficient conditions on the Banach spaces E and F in order to obtain the spaceability of the set of all linear operators from E into F which are q-compact but not p-compact. Also, under similar conditions over E, we prove that this set contains (up to the null operator) a copy of ℓs whenever F=ℓs. Finally, we give some applications of our previous results to show the spaceability of some sets formed by non-linear mappings (polynomial and Lipschitz) which are q-compact but not p-compact. The spaceability in the space of holomorphic mappings determined by p-compact sets is also considered.

Asymmetric Pair-Merger Analysis in English Preposition Stranding

In this paper I explain a well-known grammatical contrast that has been studied in the framework of Generative Grammar: the contrast between arguments and adjuncts in the preposition stranding of Wh-Questions. I make use of some recent minimalist studies: the Labeling Algorithm (LA) and the external Pair-Merger analysis based on LA. I also show that the grammaticality of heavy DP shift (HDPS) constructions, which have the same syntactic properties as Wh-questions but do not show the contrast between arguments and adjuncts in preposition stranding, can be adequately explained by the above analysis and some additional assumptions in Phase Theory. Finally, I will show that null operator (NOp) analysis is useful for the grammaticality of parasitic gap (PG) constructions, which at first glance may seem to be an empirical problem for the framework of this paper.

Physics design of new lower tungsten divertor for long-pulse high-power operations in EAST

A new lower tungsten divertor has been developed and installed in the EAST superconducting tokamak to replace the previous graphite divertor with power handling capability increasing from <2 MW m−2 to ∼10 MW m−2, aiming at achieving long-pulse H-mode operations in a full metal wall environment with the steady-state divertor heat flux of ∼10 MW m−2. A new divertor concept, ‘corner slot’ (CS) divertor, has been employed. By using the ‘corner effect’, a strongly dissipative divertor with the local buildup of high neutral pressure near the corner can be achieved, so that stable detachment can be maintained across the entire outer target plate with a relatively lower impurity seeding rate, at a separatrix density compatible with advanced steady-state core scenarios. These are essential for achieving efficient current drive with low-hybrid waves, a low core impurity concentration and thus a low loop voltage for fully non-inductive long-pulse operations. Compared with the highly closed small-angle-slot divertor in DIII-D, the new divertor in EAST exhibits the following merits: (1) a much simpler geometry with integral cassette body structure, combining vertical and horizontal target plates, which are more suitable for actively water-cooled W/Cu plasma facing components, facilitating installation precision control for minimizing surface misalignment, achieving high engineering reliability and lowering the capital cost as well; (2) it has much greater flexibility in magnetic configurations, allowing for the position of the outer strike point on either vertical or horizontal target plates to accommodate a relatively wide triangularity range, δ l = 0.4–0.6, thus enabling to explore various advanced scenarios. A water-cooled copper in-vessel coil has been installed under the dome. Five supersonic molecular beam injection systems have been mounted in the divertor to achieve faster and more precise feedback control of the gas injection rate. Furthermore, this new divertor allows for double null divertor operation and slowly sweeping the outer strike point across the horizontal and vertical target plates to spread the heat flux for long-pulse operations. Preliminary experimental results demonstrate the ‘corner effect’ and are in good agreement with simulations using SOLPS-ITER code including drifts. The EAST new divertor provides a test-bed for the closed divertor concept to achieve steady-state detachment operation at high power. Next step, a more closed divertor, ‘sharp-cornered slot’ divertor, building upon the current CS divertor concept, has been proposed as a candidate for the EAST upper divertor upgrade.

Attributive subcomparatives in Japanese

This paper aims to explain the difference in grammaticality between Japanese attributive subcomparatives with quantity adjectives (e.g., ooku/takusan ‘many’) and those with non-quantity adjectives (e.g., omosiroi ‘interesting’). My analysis assumes that Japanese clausal comparatives involve degree abstraction (Shimoyama 2012, see also Bhatt and Takahashi 2011). Degree abstraction is generally assumed to require movement of a null degree operator. In the case of attributive clausal comparatives, the movement takes place from the left branch position. If no operation that alleviates a left branch island violation is available, we would expect that the resulting sentences would be ungrammatical. I propose that in Japanese, quantifier float can play a role in ameliorating extraction out of the left branch islands. More specifically, I argue that (i) Japanese attributive subcomparatives with quantity adjectives involve quantifier float of the quantity adjectives, and that (ii) quantifier float carries the degree operators associated with the adjectives to a position where degree operator movement can originate.

ON CAUCHY-RIEMANN STRUCTURES AND THE GENERAL EVEN ORDER STRUCTURE

The present paper aims to study the Cauchy-Riemann structures and the general even order structure and find the general even order structure that acts on complementary distributions and as an almost complex structure and a null operator, respectively. We also discuss integrability conditions and prove certain theorems on the Cauchy-Riemann structures and the general even order structure. Moreover, we construct examples of it.