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This article introduces two new measures for authorship attribution - Rank-Turbulence Delta and Jensen-Shannon Delta - which generalise Burrows's classical Delta by applying distance functions designed for probabilistic distributions. We first set out the theoretical basis of the measures, contrasting centred and uncentred z-scoring of word-frequency vectors and re-casting the uncentred vectors as probability distributions. Building on this representation, we develop a token-level decomposition that renders every Delta distance numerically interpretable, thereby facilitating close reading and the validation of results. The effectiveness of the methods is assessed on four literary corpora in English, German, French and Russian. The English, German and French datasets are compiled from Project Gutenberg, whereas the Russian benchmark is the SOCIOLIT corpus containing 639 works by 89 authors spanning the eighteenth to the twenty-first centuries. Rank-Turbulence Delta attains attribution accuracy comparable with Cosine Delta; Jensen-Shannon Delta consistently matches or exceeds the performance of canonical Burrows's Delta. Finally, several established attribution algorithms are re-eval

Research Article| September 01, 1987 Fan-deltas and braid deltas: Varieties of coarse-grained deltas JOHN G. McPHERSON; JOHN G. McPHERSON 1Mobil Research and Development Corporation, Dallas Research Laboratory, P.O. Box 819047 Dallas, Texas 75381 Search for other works by this author on: GSW Google Scholar GANAPATHY SHANMUGAM; GANAPATHY SHANMUGAM 1Mobil Research and Development Corporation, Dallas Research Laboratory, P.O. Box 819047 Dallas, Texas 75381 Search for other works by this author on: GSW Google Scholar RICHARD J. MOIOLA RICHARD J. MOIOLA 1Mobil Research and Development Corporation, Dallas Research Laboratory, P.O. Box 819047 Dallas, Texas 75381 Search for other works by this author on: GSW Google Scholar Author and Article Information JOHN G. McPHERSON 1Mobil Research and Development Corporation, Dallas Research Laboratory, P.O. Box 819047 Dallas, Texas 75381 GANAPATHY SHANMUGAM 1Mobil Research and Development Corporation, Dallas Research Laboratory, P.O. Box 819047 Dallas, Texas 75381 RICHARD J. MOIOLA 1Mobil Research and Development Corporation, Dallas Research Laboratory, P.O. Box 819047 Dallas, Texas 75381 Publisher: Geological Society of America First Online: 01 Jun 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Geological Society of America GSA Bulletin (1987) 99 (3): 331–340. https://doi.org/10.1130/0016-7606(1987)99<331:FABDVO>2.0.CO;2 Article history First Online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation JOHN G. McPHERSON, GANAPATHY SHANMUGAM, RICHARD J. MOIOLA; Fan-deltas and braid deltas: Varieties of coarse-grained deltas. GSA Bulletin 1987;; 99 (3): 331–340. doi: https://doi.org/10.1130/0016-7606(1987)99<331:FABDVO>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract Two types of coarse-grained deltas are recognized: fan-deltas and braid deltas. Fan-deltas are gravel-rich deltas formed where an alluvial fan is deposited directly into a standing body of water from an adjacent highland. They occupy a space between the highland (usually a fault-bounded margin) and the standing body of water. In contrast, braid deltas (here introduced) are gravel-rich deltas that form where a braided fluvial system progrades into a standing body of water. Braid deltas have no necessary relationship with alluvial fans, as exemplified by fluvioglacial braid deltas. Braid deltas have previously been classified as fan-deltas even though the geomorphic and sedimentologic settings of the two systems can be vastly different. Braid deltas are a common present-day geomorphic feature and are abundant in the geological record.Fan-deltas and braid deltas can be distinguished in the rock record by distinctive subaerial components of these depositional systems; the shoreline and subaqueous components of both are similar. Fan-delta sequences have a subaerial component that is an alluvial-fan facies comprising interbedded sheetflood, debris-flow, and braided-channel deposits. Fan-deltas produce small (a few tens of square kilometres), wedge-shaped bodies of sediment, commonly displaying high variability in paleocurrent patterns and abrupt changes in facies. The deposits are generally very coarse grained (with large out-sized clasts), very poorly sorted, matrix-rich, polymictic, heterolithic, partially cemented by penecontemporaneous carbonate, and have low porosity and permeability. Braid-deltas, in contrast, have a subaerial component consisting entirely of braided-river or braidplain facies. Their deposits display better sorting, roundness, and clast orientation than do fan-delta sediments; they lack a muddy matrix; they display size grading and bar migration; they commonly have a sheet geometry with high lateral continuity (tens to hundreds of square kilometres); and they exhibit moderate to high porosity and permeability. Valuable paleogeographic and tectonic information concerning the proximity of highlands and major fault zones may be misinterpreted or lost if these two coarse-grained deltaic systems are not differentiated. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

We explore what fraction of delta sunspots in which the polarity inversion line (PIL) is sharp in photospheric magnetograms are made from a writhe kink in an emerging twisted flux rope. We searched simultaneous full-disk magnetograms and continuum images from Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO) to find 28 random sharp-PIL delta sunspots that are born well on the disk. Only one of these is made from a single newly emerged bipolar magnetic region (BMR) and therefore is a candidate for being made from a single emerging writhe-kinked flux rope. That outcome indicates that few, if any, sharp-PIL delta sunspots are made by a single emerging writhe-kinked flux rope. That is the main new finding of this paper. Each of the other 27 is made by merging of two or more emerging or emerged BMRs. We name delta-sunspot genesis from a single BMR Type I genesis. We identify another three genesis types among the other 27 delta sunspots: Type II, Type III, and Type IV. We present an observed example genesis for each of the four genesis types, and for each example present schematic drawings depicting our scenario(s) for the cause of that example genesis. The core

In this paper, we introduce the concept of various types fuzzy delta $(δ)$ compactness such as Quasi fuzzy delta compact, Quasi fuzzy countably delta compact, Weakly fuzzy delta compact, $a$-delta compact, Strong fuzzy delta compact, Ultra fuzzy delta compact and Fuzzy delta compact and characterize these types of fuzzy delta compactness using the notion of fuzzy upper limit of net of some types of delta $(δ)$ closed sets.

Attention Residuals replace standard additive residual connections with learned softmax attention over previous layer outputs, enabling selective cross-layer routing. However, standard Attention Residuals still attend over cumulative hidden states in previous layers, which are highly redundant. We show that this redundancy leads to routing collapse in deeper layers: attention weights become low-contrast and closer to uniform (max weight ${\approx}$0.2), limiting the model's ability to select informative states in previous layers. This raises a key but underexplored design question: what layer-wise representations should be routed in Attention Residuals? To answer this question, we propose Delta Attention Residuals, which attend over deltas -- the change introduced by each sublayer ($\mathbf{v}_i = \mathbf{h}_{i+1} - \mathbf{h}_i$) -- instead of cumulative states. Delta representations are structurally diverse and yield higher-contrast attention distributions (max weight ${\approx}$0.6), enabling more selective and effective routing across layers. This principle applies at both per-sublayer and block granularity. Across all tested scales (220M--7.6B), Delta Attention Residuals consi

Transformer residual streams evolve by additive accumulation: each layer appends a feature update to a shared hidden state, but has no direct mechanism for replacing content that has become obsolete or conflicting. We introduce Deep Delta Learning (DDL), a residual update rule that preserves the identity path while giving every layer the ability to selectively rewrite residual content. DDL reads the current state along a learned direction, compares it with a learned target value, and writes back a gated correction along the same direction. When the gate is closed, the update reduces to the identity; when the gate is fully open, the selected component is overwritten, yielding a depth-wise delta-rule generalization of standard residual addition. We integrate DDL in decoder-only language models with both scalar and expanded residual states, while keeping attention and MLP sublayers at the original compute width. Controlled pretraining and downstream evaluations show that residual rewrite operations improve language modeling quality relative to pure additive accumulation introduced in ResNet, suggesting that a learned delta-rule update is an effective mechanism for managing Transformer

Linear Transformers have gained attention as efficient alternatives to standard Transformers, but their performance in retrieval and long-context tasks has been limited. To address these limitations, recent work has explored two distinct mechanisms: gating for adaptive memory control and the delta update rule for precise memory modifications. We observe that these mechanisms are complementary: gating enables rapid memory erasure while the delta rule facilitates targeted updates. Building on this insight, we introduce the gated delta rule and develop a parallel training algorithm optimized for modern hardware. Our proposed architecture, Gated DeltaNet, consistently surpasses existing models like Mamba2 and DeltaNet across multiple benchmarks, including language modeling, common-sense reasoning, in-context retrieval, length extrapolation, and long-context understanding. We further enhance performance by developing hybrid architectures that combine Gated DeltaNet layers with sliding window attention or Mamba2 layers, achieving both improved training efficiency and superior task performance.

Delta lenses are functors equipped with a functorial choice of lifts, generalising the notion of split opfibration. In this paper, we introduce a Grothendieck construction (or category of elements) for delta lenses, thus demonstrating a correspondence between delta lenses and certain lax double functors into the double category of sets, functions, and split multivalued functions. We show that the double category of split multivalued functions admits a universal property as a certain kind of limit, and inherits many nice properties from the double category of spans. Applications of this construction to the theory of delta lenses are explored in detail.

We compute the delta power operation for morava E-theory of height 2 at the prime 3. The delta power operation was defined using the notion of higher semi additivity by Shachar Carmeli, Tomer M. Schlank and Lior Yanovski. We briefly survey the basic definitions in higher semi-additivity. Using explicit formulas for moduli spaces of elliptic curves and computations done by Y. Zhu for the total power operation we provide an explicit formula for the delta power operation. We obtain the numerical result that the delta operation of a polynomial is a polynomial which can be explained by a certain connection which was described by M. Hopkins, C. Rezk and later N. Stapleton between similar operations and the Hecke action on the functions on the moduli space of elliptic curves.

The category fat Delta, introduced by J. Kock, is a modification of the simplex category where the degeneracies behave weakly. The objective of this note is to provide tools for working with fat Delta. In particular, we identify three types of morphisms: degenerated, standard and vertical faces, and establish six relations between these classes. We then show that fat Delta is generated by these morphisms and relations.

Abstract A delta is a partially subaerial, contiguous mass of sediment deposited around the point where a river enters a standing body of water. A deltaic system is a three-dimensional rock-stratigraphic unit composed of many adjacent delta lobes deposited as a part of a major cycle of terrigenous sediment influx. Delta morphology and internal stratigraphy are primarily the product of an interplay between fluvial sediment input and reworking of sediment by marine or lacustrine processes. Although sources of marine energy include oceanic and wind-generated currents, density currents, gravitational potential, tidal currents, storm surge, and wave surge, deltaic progradation is modified primarily by tidal currents and wave surge. Marine deltas can thus be characterized in terms of three end-member types: (1) fluvial-dominated deltas, (2) wave-dominated deltas, and (3) tide-dominated deltas. Modern fluvial-dominated deltas include the birdfoot lobe of the Holocene Mississippi Delta system and the Po and Danube deltas. The Rhone and Sao Francisco are typical wave-dominated deltas. The Ganges-Brahmaputra, Fly, and Colorado deltas are of the tide-dominated type. Gravity induced sediment transport tends to remove sediment basinward from the delta system into slope, submarine fan, and basin floor environments which are best considered separate depositional systems. Within deltaic depositional systems, longterm evolutionary trends can be recognized and interpreted in terms of response to changing process intensity. Pennsylvanian deltas of north-central Texas changed from fluvial-dominated elongate to wave-influenced or even wave-dominated lobate types as they prograded across a shallow platform into deeper, open marine water. Early Eocene (Wilcox) and Miocene clastic cycles of the Gulf Coast Tertiary basin evolved from fluvial-dominated elongate and lobate deltas of the regressive phase to wave-dominated deltas of the transgressive phase of the cycle.

By applying a relativistic mean-field description of neutron star matter with density dependent couplings, we analyse the properties of two different matter compositions: nucleonic matter with delta baryons and nucleonic matter with hyperons and delta baryons. The delta-meson couplings are allowed to vary within a wide range of values obtained by experimental data, while the hyperon-meson couplings are fitted to hypernuclear properties. Neutron star properties with no deconfinement phase transition are studied. It is verified that many models are excluded because the effective nucleon mass becomes zero before the maximum mass configuration is attained. Hyperon-free with delta-dominated composition compact stars are possible, the deltic stars. It is found that with a convenient choice of parameters the existence of deltic stars with 80% of delta baryons at the center of the star is possible. However, the presence of hyperons lowers the delta baryon fraction to values below 20% at the center and below 30% at 2-3 saturation densities. It is discussed that in the presence of delta baryons, the hyperon softening is not so drastic because deltas couple more strongly to the $ω$-meson, and

The Delta-Delta component of the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the relativistic field theory model of the deuteron. For the probability of the Delta-Delta component of the deuteron we give P(Delta-Delta) = 0.08 %. This prediction agrees good with the experimental estimate P(Delta-Delta) &lt; 0.4 % at 90 % of CL (D. Allasia et al., Phys. Lett. B174 (1986) 450).

Classical Gončarov polynomials are polynomials which interpolate derivatives. Delta Gončarov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gončarov polynomials and univariate delta Gončarov polynomials to the multivariate setting using umbral calculus. After introducing systems of delta operators, we define multivariate delta Gončarov polynomials, show that the associated interpolation problem is always solvable, and derive a generating function (an Appell relation) for them. We show that systems of delta Gončarov polynomials on an interpolation grid $Z \subseteq \mathbb{R}^d$ are of binomial type if and only if $Z = A\mathbb{N}^d$ for some $d\times d$ matrix $A$. This motivates our definition of delta Abel polynomials to be exactly those delta Gončarov polynomials which are based on such a grid. Finally, compact formulas for delta Abel polynomials in all dimensions are given for separable systems of delta operators. This recovers a former result for classical bivariate Abel polynomials and extends previous partial results for classical trivariate Abe

Large Language Models (LLMs) are increasingly being used in real-world applications. However, concerns about the reliability of the content they generate persist, as it frequently deviates from factual correctness or exhibits deficiencies in logical reasoning. This paper proposes a novel decoding strategy aimed at enhancing both factual accuracy and inferential reasoning without requiring any modifications to the architecture or pre-trained parameters of LLMs. Our approach adjusts next-token probabilities by analyzing the trajectory of logits from lower to higher layers in Transformers and applying linear regression. We find that this Decoding by Logit Trajectory-based approach (DeLTa) effectively reinforces factuality and reasoning while mitigating incorrect generation. Experiments on TruthfulQA demonstrate that DeLTa attains up to a 4.9% improvement over the baseline. Furthermore, it enhances performance by up to 8.1% on StrategyQA and 7.3% on GSM8K, both of which demand strong reasoning capabilities.

The probability P(Delta-Delta) to find the Delta-Delta component inside the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the Nambu-Jona-Lasinio model of light nuclei. We obtain P(Delta-Delta) = 0.3%. This prediction agrees good with the experimental estimate P(Delta-Delta) &lt; 0.4% at 90% of CL (D. Allasia et al., Phys. Lett. B174 (1986) 450).

Delta lenses are functors equipped with a suitable choice of lifts, and are used to model bidirectional transformations between systems. In this paper, we construct an algebraic weak factorisation system whose R-algebras are delta lenses. Our approach extends a semi-monad for delta lenses previously introduced by Johnson and Rosebrugh, and generalises to any suitable category equipped with an orthogonal factorisation system and an idempotent comonad. We demonstrate how the framework of an algebraic weak factorisation system provides a natural setting for understanding the lifting operation of a delta lens, and also present an explicit description of the free delta lens on a functor.

Tracking dense 3D motion from monocular videos remains challenging, particularly when aiming for pixel-level precision over long sequences. We introduce DELTA, a novel method that efficiently tracks every pixel in 3D space, enabling accurate motion estimation across entire videos. Our approach leverages a joint global-local attention mechanism for reduced-resolution tracking, followed by a transformer-based upsampler to achieve high-resolution predictions. Unlike existing methods, which are limited by computational inefficiency or sparse tracking, DELTA delivers dense 3D tracking at scale, running over 8x faster than previous methods while achieving state-of-the-art accuracy. Furthermore, we explore the impact of depth representation on tracking performance and identify log-depth as the optimal choice. Extensive experiments demonstrate the superiority of DELTA on multiple benchmarks, achieving new state-of-the-art results in both 2D and 3D dense tracking tasks. Our method provides a robust solution for applications requiring fine-grained, long-term motion tracking in 3D space.

Event cameras and LiDARs provide complementary yet distinct data: respectively, asynchronous detections of changes in lighting versus sparse but accurate depth information at a fixed rate. To this day, few works have explored the combination of these two modalities. In this article, we propose a novel neural-network-based method for fusing event and LiDAR data in order to estimate dense depth maps. Our architecture, DELTA, exploits the concepts of self- and cross-attention to model the spatial and temporal relations within and between the event and LiDAR data. Following a thorough evaluation, we demonstrate that DELTA sets a new state of the art in the event-based depth estimation problem, and that it is able to reduce the errors up to four times for close ranges compared to the previous SOTA.