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We study 27-day variations of the galactic cosmic ray (GCR) intensity for 2005- 2008 period of the solar cycle #23. We use neutron monitors (NMs) data corrected and uncorrected for geomagnetic disturbances. Besides the limited time intervals when the 27-day variations are clearly established, always exist some feeble 27-day variations in the GCR 5 intensity related to the constantly present weak heliolongitudinal asymmetry in the heliosphere. We calculate the amplitudes of the 27-day variation of the GCR intensity based on the NMs data corrected and uncorrected for geomagnetic disturbances. We show that these amplitudes do not differ for NMs with cut-off rigidities smaller than 4-5 GV comparing with NMs of higher cut-off rigidities. Rigidity spectrum of the 27-day variation of the GCR intensity found in the uncorrected data is soft while it is hard in the case of the corrected data. For both cases exists definite tendency of softening the temporal changes of the 27-day variation's rigidity spectrum in period of 2005 to 2008 approaching the minimum of solar activity. We believe that a study of the 27-day variation of the GCR intensity based on the data uncorrected for geomagnetic disturbances should be carried out by NMs with cut-off rigidities smaller than 4-5 GV.
http://arxiv.org/abs/1509.05738v1
The temporal evaluation of the 27-day variation of the three dimensional (3D) galactic cosmic ray (GCR) anisotropy has been studied for 1965-2014. 3D anisotropy vector was obtained based on the neutron monitors and Nagoya muon telescopes data. We analyze the 27-day variation of the (1) two dimensional (2D) GCR anisotropy in the ecliptic plane, and (2) north-south anisotropy normal to the ecliptic plane. Studying the time line of the 27-day variation of the 2D GCR anisotropy, we confirm that the average amplitude in the minimum epoch of solar activity is polarity dependent, as it is expected from the drift theory. The amplitude in the negative polarity epochs is less as we had shown before. The feeble 11-year variation connected with solar cycle and strong 22-year pattern connected with solar magnetic cycle is visible in the 27-day variation of the 2D anisotropy for 1965-2014. We show that the 27-day variation of the GG index (being a measure of the north-south asymmetry) varies in accordance to solar cycle with a period of 11-years, being in good agreement with the 27-day variation of the At component of the GCR anisotropy calculated by the IZMIRAN group. Detailed analysis are presented for the solar minimum 2007-2008 of solar cycle no.23 and solar maximum 2013-2015 of solar cycle no 24. In the solar cycle no. 24 GG index, calculated by Nagoya telescopes data, is highly anticorrelated with By component of the interplanetary magnetic field (IMF) and shows a clear recurrent changes related to the Sun's rotation.
http://arxiv.org/abs/1509.05770v1
Supercontinuum generation (SCG) with spectral coverage across the full visible and ultraviolet (UV) ranges is crucial for optical clocks, quantum computing and sensing. However, achieving such SCG in nanophotonic platforms is challenging due to the difficulties in spectrum broadening. Here, Such ultrabroad-bandwidth SCG was demonstrated in thin-film lithium niobate (TFLN) nanophotonic waveguides by dispersion management, without periodic poling for spectral broadening. Anomalous-dispersion waveguides were designed in the telecom band, simultaneously enabling dispersive wave emergence, modal-matched second harmonic generation, and third harmonic generation for spectrum broadening. Moreover, MgO was intentionally doped to mitigate the photorefractive effect of lithium niobate, which frequently results in un-sustained spectrum broadening and in turn limits the accessible SCG coverage. By leveraging photolithography assisted chemo-mechanical etching, low-loss MgO doped TFLN nanophotonic waveguides were fabricated. As a result, thanks to the utilization of the strong second-order and third-order nonlinear processes, gap-free 2.7-octave SCG spanning from 330 nm to 2250 nm was observed by pumping the waveguide with a 1550-nm femtosecond pulsed laser with 0.687 nJ, agreeing well with numerical simulation. This spectral coverage represents the state of the art in TFLN platforms without fine microdomains, and even close to the record in sophisticated chirped periodically poled TFLN waveguides.
https://arxiv.org/abs/2505.12438v1
The paper proposes open problems in classical Kolmogorov complexity. Each problem is presented with background information and thus the article also surveys some recent studies in the area.
https://arxiv.org/abs/2203.15109v1
We study the decomposition into $SU(N)$ irreducible representations (irreps) of the tensor product $27 \otimes 27$, where $27$ is the highest-dimensional $SU(N)$ irrep present in a two-gluon system, and explicitly construct all Hermitian projectors on these irreps, as well as transition operators between them. This yields an explicit basis of the complete $27\otimes 27$ color space (defined as the space of $27\otimes 27\to 27 \otimes 27$ color maps) in terms of orthogonal multiplets. This study shows that even complex color structures can be addressed, with the help of the birdtrack pictorial technique, using only elementary tools. In particular, we highlight the usefulness of the quadratic Casimir operator, whose eigenspaces allow efficient filtering of all projectors and transition operators, and of the permutation operators that further improve this filtering. The product $27\otimes 27$ also has an interesting feature: three equivalent irreps $27$ appear in the decomposition, two of which are symmetric and can therefore be distinguished neither by the quadratic Casimir operator nor by their symmetry under permutation. In this case, it is convenient to use Clebsch-Gordan coefficients to derive the two associated, symmetric projectors. The latter are not uniquely determined (only their sum is), and we give the set of all solutions. Finally, we explicitly derive the soft anomalous dimension matrix associated with $27\otimes 27\to 27\otimes 27$, whose block-diagonal main structure is easy to understand, but whose detailed spectrum properties remain intriguing. The approach presented for $27 \otimes 27 \to 27 \otimes 27$ could in principle be applied to any product of $SU(N)$ irreps, and eventually automated.
https://arxiv.org/abs/2504.11362v1
Predicting accurate NMR chemical shieldings relies upon cancellation of different types of error in the ab initio methodology used to calculate the shielding tensor of the analyte of interest and the reference. Often the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects, is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation $\text{Al}(\text{H}_{2}\text{O})_{6}^{3+}$ , accounting for ab initio intrinsic errors. However, the fact that this analyte is used as a reference for the chemically distinct tetrahedral anion $\text{Al}(\text{OH})_{4}^{-}$ inspires the study of how these errors cancel in an attempt to understand the limits of predictive capability for accurately determining $^{27}\text{Al }$ shielding in $\text{Al}(\text{OH})_{4}^{-}$. In this work, we estimate the absolute shielding of $^{27}\text{Al }$ nucleus in $\text{Al}(\text{OH})_{4}^{-}$ at the coupled cluster level (515.1 $\pm$ 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets treatment has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab-initio molecular dynamics. The contribution of each type of intrinsic error is assessed for $\text{Al}(\text{H}_{2}\text{O})_{6}^{3+}$ and $\text{Al}(\text{OH})_{4}^{-}$ ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the $^{27}\text{Al }$ chemical shift of $\text{Al}(\text{OH})_{4}^{-}$ from first principles.
http://arxiv.org/abs/2001.00107v1
We propose a simple, yet effective, approach towards inducing multilingual taxonomies from Wikipedia. Given an English taxonomy, our approach leverages the interlanguage links of Wikipedia followed by character-level classifiers to induce high-precision, high-coverage taxonomies in other languages. Through experiments, we demonstrate that our approach significantly outperforms the state-of-the-art, heuristics-heavy approaches for six languages. As a consequence of our work, we release presumably the largest and the most accurate multilingual taxonomic resource spanning over 280 languages.
http://arxiv.org/abs/1704.07624v2
We describe the construction and characterization of the 280 GHz bolometric focal plane units (FPUs) to be deployed on the second flight of the balloon-borne SPIDER instrument. These FPUs are vital to SPIDER's primary science goal of detecting or placing an upper limit on the amplitude of the primordial gravitational wave signature in the cosmic microwave background (CMB) by constraining the B-mode contamination in the CMB from Galactic dust emission. Each 280 GHz focal plane contains a 16 x 16 grid of corrugated silicon feedhorns coupled to an array of aluminum-manganese transition-edge sensor (TES) bolometers fabricated on 150 mm diameter substrates. In total, the three 280 GHz FPUs contain 1,530 polarization sensitive bolometers (765 spatial pixels) optimized for the low loading environment in flight and read out by time-division SQUID multiplexing. In this paper we describe the mechanical, thermal, and magnetic shielding architecture of the focal planes and present cryogenic measurements which characterize yield and the uniformity of several bolometer parameters. The assembled FPUs have high yields, with one array as high as 95% including defects from wiring and readout. We demonstrate high uniformity in device parameters, finding the median saturation power for each TES array to be ~3 pW at 300 mK with a less than 6% variation across each array at one standard deviation. These focal planes will be deployed alongside the 95 and 150 GHz telescopes in the SPIDER-2 instrument, slated to fly from McMurdo Station in Antarctica in December 2018.
http://arxiv.org/abs/1711.04169v2
In a companion paper, we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)
http://arxiv.org/abs/1512.03433v2
In the past, the mirror asymmetry parameter has been proposed as a probing mechanism for the presence of beyond the Standard Model second-class currents in nuclear beta decay transitions. However, this was hindered by large uncertainties in the required nuclear structure correction terms. Recently, a new calculation of these corrections attempted, but could not fully explain the negative mirror asymmetry between the $^{28}$Al($\beta^-$)$^{28m}$Si and $^{28}$P($\beta^+$)$^{28m}$Si decays. To put the mirror asymmetry parameter on a more solid footing, the half-life of $^{28}$Al was measured for the first time using a radioactive ion beam at the Nuclear Science Laboratory of the University of Notre Dame. The new result, $t_{1/2}=$134.432(34) s, is consistent with most of the past data except for one highly discrepant measurement. The new mirror asymmetry parameter of -3.5(10)$\%$ obtained still does not agree with nuclear structure calculations.
https://arxiv.org/abs/2505.01722v1
In the upcoming 5G communication, the millimeter-wave (mmWave) technology will play an important role due to its large bandwidth and high data rate. However, mmWave frequencies have higher free-space path loss (FSPL) in line-of-sight (LOS) propagation compared to the currently used sub-6 GHz frequencies. What is more, in non-line-of-sight (NLOS) propagation, the attenuation of mmWave is larger compared to the lower frequencies, which can seriously degrade the performance. It is therefore necessary to investigate mmWave propagation characteristics for a given deployment scenario to understand coverage and rate performance for that environment. In this paper, we focus on 28 GHz wideband mmWave signal propagation characteristics at Johnston Regional Airport (JNX), a local airport near Raleigh, NC. To collect data, we use an NI PXI based channel sounder at 28 GHz for indoor, outdoor, and indoor-to-outdoor scenarios. Results on LOS propagation, reflection, penetration, signal coverage, and multi-path components (MPCs) show a lower indoor FSPL, a richer scattering, and a better coverage compared to outdoor. We also observe high indoor-to-outdoor propagation losses.
https://arxiv.org/abs/2101.02599v1
This paper presents small-scale fading measurements for 28 GHz outdoor millimeter-wave ultrawideband channels using directional horn antennas at the transmitter and receiver. Power delay profiles were measured at half-wavelength spatial increments over a local area (33 wavelengths) on a linear track in two orthogonal receiver directions in a typical base-to-mobile scenario with fixed transmitter and receiver antenna beam pointing directions. The voltage path amplitudes are shown to follow a Rician distribution, with K-factor ranging from 9 - 15 dB and 5 - 8 dB in line of sight (LOS) and non-line of sight (NLOS) for a vertical-to-vertical co-polarized antenna scenario, respectively, and from 3 - 7 dB in both LOS and NLOS vertical-to-horizontal cross-polarized antenna scenario. The average spatial autocorrelation functions of individual multipath components reveal that signal amplitudes reach a correlation of 0 after 2 and 5 wavelengths in LOS and NLOS co-polarized V-V antenna scenarios. The models provided are useful for recreating path gain statistics of millimeter-wave wideband channel impulse responses over local areas, for the study of multi-element antenna simulations and channel estimation algorithms.
http://arxiv.org/abs/1511.06938v2
To fully exploit the millimeter-wave bands for the fifth generation cellular systems, an accurate understanding of the channel propagation characteristics is required, and hence extensive measurement campaigns in different environments are needed. In this paper, we use a rotated directional antenna-based channel sounder for measurements at 28 GHz in large indoor environments at a library setting. We present models for power angular-delay profile and large-scale path loss based on the measurements over distances ranging from 10 m to 50 m. In total, nineteen different line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios are considered, including the cases where the transmitter and the receiver are placed on different floors. Results show that the close-in free space reference distance and the floating intercept path loss models both perform well in fitting the empirical data. The path loss exponent obtained for the LOS scenarios is found to be very close to that of the free space path loss model.
http://arxiv.org/abs/1910.08632v1
This paper presents results from a comprehensive measurement campaign conducted at 28 GHz inside a container canyon within a commercial port environment. The measurements are performed at various points inside the container canyon, considering two types of container stacking and two different Transmitter (TX) locations, using a narrowband channel sounder equipped with a rotating horn antenna. The measurements are used to evaluate the azimuthal spectrum and spatial correlation, as well as the impact of a vehicle inside a canyon on these parameters. Further, the measurement data is utilized to validate a simulation setup from which the path loss and the elevation spectrum inside the canyon is obtained. Lastly, a propagation model inside the canyon is hypothesized and shown to be consistent with the measurements. The analysis show a low path loss compared to free space, as well as a high angular spread and short spatial correlation.
https://arxiv.org/abs/2309.02810v1
We present measurements of the 28 GHz self-interference channel for full-duplex sectorized multi-panel millimeter wave (mmWave) systems, such as integrated access and backhaul. We measure the isolation between the input of a transmitting phased array panel and the output of a co-located receiving phased array panel, each of which is electronically steered across a number of directions in azimuth and elevation. In total, nearly 6.5 million measurements were taken in an anechoic chamber to densely inspect the directional nature of the coupling between 256-element phased arrays. We observe that highly directional mmWave beams do not necessarily offer widespread high isolation between transmitting and receiving arrays. Rather, our measurements indicate that steering the transmitter or receiver away from the other tends to offer higher isolation but even slight steering changes can lead to drastic variations in isolation. These measurements can be useful references when developing mmWave full-duplex solutions and can motivate a variety of future topics including beam/user selection and beamforming codebook design.
https://arxiv.org/abs/2203.02809v1
This paper reports the first cryogenic characterization of 28nm Fully-Depleted-SOI CMOS technology. A comprehensive study of digital/analog performances and body-biasing from room to the liquid helium temperature is presented. Despite a cryogenic operation, effectiveness of body-biasing remains unchanged and provides an excellent $V_{TH}$ controllability. Low-temperature operation enables higher drive current and a largely reduced subthreshold swing (down to 7mV/dec). FDSOI can provide a valuable approach to cryogenic low-power electronics. Applications such as classical control hardware for quantum processors are envisioned.
http://arxiv.org/abs/2002.07070v1
We report the generation of an optical frequency comb featuring 28 THz bandwidth, sustained by a single 80 fs cavity soliton recirculating in a fiber Fabry-Perot resonator. This large spectrum is comparable to frequency combs obtained with microresonators operating in the anomalous dispersion regime. Thanks to the compact design and the easy coupling of the resonator, cavity solitons can be generated in an all-fiber experimental setup with a continuous wave pumping scheme. We also observe the generation of a dispersive wave at higher frequencies which is supported by higher-order dispersion. These observations align remarkably well with both numerical simulations and the established theory of cavity solitons.
https://arxiv.org/abs/2401.12858v1
There is significant interest in the models for production of short gamma-ray bursts. Until now, the number of known short gamma-ray bursts with multi-wavelength afterglows has been small. While the {\it Fermi} Gamma-Ray Burst Monitor detects many gamma-ray bursts relative to the Neil Gehrels {\it Swift} Observatory, the large localization regions makes the search for counterparts difficult. With the Zwicky Transient Facility recently achieving first light, it is now fruitful to use its combination of depth ($m_\textrm{AB} \sim 20.6$), field of view ($\approx$ 47 square degrees), and survey cadence (every $\sim 3$ days) to perform Target of Opportunity observations. We demonstrate this capability on GRB 180523B, which was recently announced by the {\it Fermi} Gamma-Ray Burst Monitor as a short gamma-ray burst. ZTF imaged $\approx$ 2900\,square degrees of the localization region, resulting in the coverage of 61.6\,\% of the enclosed probability over 2 nights to a depth of $m_\textrm{AB} \sim 20.5$. We characterized 14 previously unidentified transients, and none were found to be consistent with a short gamma-ray burst counterpart. This search with the Zwicky Transient Facility shows it is an efficient camera for searching for coarsely-localized short gamma-ray burst and gravitational-wave counterparts, allowing for a sensitive search with minimal interruption to its nominal cadence.
http://arxiv.org/abs/1901.11385v1
Jupiter-family comets (JFCs) are the evolutionary products of trans-Neptunian objects (TNOs) that evolve through the giant planet region as Centaurs and into the inner solar system. Through numerical orbital evolution calculations following a large number of TNO test particles that enter the Centaur population, we have identified a short-lived dynamical Gateway, a temporary low-eccentricity region exterior to Jupiter through which the majority of JFCs pass. We apply an observationally based size distribution function to the known Centaur population and obtain an estimated Gateway region population. We then apply an empirical fading law to the rate of incoming JFCs implied by the the Gateway region residence times. Our derived estimates are consistent with observed population numbers for the JFC and Gateway populations. Currently, the most notable occupant of the Gateway region is 29P/Schwassmann-Wachmann 1 (SW1), a highly active, regularly outbursting Centaur. SW1's present-day, very-low-eccentricity orbit was established after a 1975 Jupiter conjunction and will persist until a 2038 Jupiter conjunction doubles its eccentricity and pushes its semi-major axis out to its current aphelion. Subsequent evolution will likely drive SW1's orbit out of the Gateway region, perhaps becoming one of the largest JFCs in recorded history. The JFC Gateway region coincides with a heliocentric distance range where the activity of observed cometary bodies increases significantly. SW1's activity may be typical of the early evolutionary processing experienced by most JFCs. Thus, the Gateway region, and its most notable occupant SW1, are critical to both the dynamical and physical transition between Centaurs and JFCs.
http://arxiv.org/abs/1908.04185v2
Centaur 29P/Schwassmann-Wachmann 1 (SW1) is a highly active object orbiting in the transitional Gateway region (Sarid et al. 2019) between the Centaur and Jupiter Family Comet regions. SW1 is unique among the Centaurs in that it experiences quasi-regular major outbursts and produces CO emission continuously; however, the source of the CO is unclear. We argue that due to its very large size (approx. 32 km radius), SW1 is likely still responding, via amorphous water ice (AWI) conversion to crystalline water ice (CWI), to the rapid change in its external thermal environment produced by its dynamical migration from the Kuiper belt to the Gateway Region at the inner edge of the Centaur region at 6 au. It is this conversion process that is the source of the abundant CO and dust released from the object during its quiescent and outburst phases. If correct, these arguments have a number of important predictions testable via remote sensing and in situ spacecraft characterization, including: the quick release on Myr timescales of CO from AWI conversion for any few km-scale scattered disk KBO transiting into the inner system; that to date SW1 has only converted between 50 to 65% of its nuclear AWI to CWI; that volume changes upon AWI conversion could have caused subsidence and cave-ins, but not significant mass wasting or crater loss on SW1; that SW1s coma should contain abundant amounts of CWI CO2-rich icy dust particles; and that when SW1 transits into the inner system within the next 10,000 years, it will be a very different kind of JFC comet.
https://arxiv.org/abs/2209.09136v2
This study introduces the AI-Accentuated Career Transitions framework, advancing beyond binary automation narratives to examine how distinct AI usage patterns reshape occupational mobility. Analyzing 545 occupations through multivariate modeling, we identify six qualitatively distinct human-AI usage patterns that differentially predict placement across job preparation zones. Our findings empirically validate the "missing middle" hypothesis: automation-focused usage strongly predicts lower job zone placement while augmentative usage predicts higher zones. Most significantly, we identify specific Knowledge, Skill, and Abilities combinations with AI usage patterns that function as "skill bridges" facilitating upward mobility. The interaction between task iteration AI usage and cognitive skills emerges as the strongest advancement predictor, creating pathways across traditionally disconnected occupational categories. Counterintuitively, despite directive AI's negative main effect, its interaction with technical knowledge positively predicts advancement in specialized domains. Comparative model testing confirms that AI usage patterns represent a distinct dimension of occupational classification that adds significant explanatory power beyond traditional skill measures. These findings reveal AI as a skill amplifier that widens capability gaps rather than an equalizing force. The 2ACT framework provides strategic guidance for workers, curriculum designers, policymakers, and organizations navigating increasingly AI-mediated career pathways.
https://arxiv.org/abs/2505.07914v1
Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$ without CM. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each elliptic curve in $\mathcal{E}$ and an edge for each $\mathbb{Q}$-isogeny of prime degree that maps one elliptic curve in $\mathcal{E}$ to another elliptic curve in $\mathcal{E}$, with the degree recorded as a label of the edge. An isogeny-torsion graph is an isogeny graph where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over $\mathbb{Q}$ of the corresponding elliptic curve. Then, the main statement of the article is a classification of the $2$-adic image of Galois that occurs at each vertex of all isogeny-torsion graphs consisting of elliptic curves defined over $\mathbb{Q}$ without CM.
https://arxiv.org/abs/2302.06094v2
Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each element of $\mathcal{E}$ and an edge for each $\mathbb{Q}$-isogeny of prime degree that maps one elliptic curve in $\mathcal{E}$ to another elliptic curve in $\mathcal{E}$, with the degree of the isogeny recorded as a label of the edge. The isogeny-torsion graph associated to $\mathcal{E}$ is the isogeny graph associated to $\mathcal{E}$ where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over $\mathbb{Q}$ of the corresponding elliptic curve. The main result of the article is a classification of the 2-adic Galois image at each vertex of the isogeny-torsion graphs whose associated $\mathbb{Q}$-isogeny class consists of elliptic curves over $\mathbb{Q}$ with complex multiplication.
https://arxiv.org/abs/2208.11649v2
We construct integral models over $p=2$ for some Shimura varieties of abelian type with parahoric level structure, extending the previous work of Kim-Madapusi, Kisin, Pappas, and Zhou. For Shimura varieties of Hodge type, we show that our integral models are canonical in the sense of Pappas-Rapoport.
https://arxiv.org/abs/2301.12981v2
This article reports on an approach to point counting on algebraic varieties over finite fields that is based on a detailed investigation of the $2$-adic orthogonal group. Combining the new approach with a $p$-adic method, we count the number of points on some $K3$ surfaces over the field $\bbF_{\!p}$, for all primes $p < 10^8$.
https://arxiv.org/abs/2202.10853v2
Using techniques of p-adic analysis, it is possible to formulate a rigorous version of the quantum mechanics (QM), in the sense of Dirac-von Neumann, consistent with the existence of the Planck length. Such a model cannot be formulated if we use R^{3} as a model for physical space. The experimental testability of physical theories at the Planck scale is currently impossible. Here, we provide an indirect, theoretical argument that shows that the p-adic QM has physical content. We show that a large class of Schr\"odinger equations describes the scaling limits of continuous-time quantum walks on graphs (stochastic automata). These quantum walks appear as fundamental tools in quantum computing. We conjecture that this interpretation is valid in a general framework. The `new theory' does not have Lorentz symmetry, and the Einstein causality is violated. This fact does not contradict the so-called no-communication theorem; such a result requires as a primary hypothesis that R^{4} be a valid model for space-time at the Planck scale. Thus, the no-communication theorem under the discreteness of the space is an open problem.
https://arxiv.org/abs/2502.16416v1
We show that for arithmetic weights with a fixed finite order character, the slopes of $U_p$ (for $p=2$) acting on overconvergent Hilbert modular forms of level $U_0(4)$ are independent of the (algebraic part of the) weight and can be obtained by a simple recipe from the classical slopes in parallel weight $3$.
http://arxiv.org/abs/1811.04799v3
In this paper we study the multiplicities and the asymptotic behaviour of the numbers of totients in the strata given by 2-adic valuation.
http://arxiv.org/abs/2005.05475v1
Properties of 2-adic valuation sequences for general quadratic polynomials with integer coefficients are determined directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.
https://arxiv.org/abs/2012.10332v4
We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
https://arxiv.org/abs/2008.12433v4
While abundant research has been conducted on improving high-level visual understanding and reasoning capabilities of large multimodal models~(LMMs), their visual quality assessment~(IQA) ability has been relatively under-explored. Here we take initial steps towards this goal by employing the two-alternative forced choice~(2AFC) prompting, as 2AFC is widely regarded as the most reliable way of collecting human opinions of visual quality. Subsequently, the global quality score of each image estimated by a particular LMM can be efficiently aggregated using the maximum a posterior estimation. Meanwhile, we introduce three evaluation criteria: consistency, accuracy, and correlation, to provide comprehensive quantifications and deeper insights into the IQA capability of five LMMs. Extensive experiments show that existing LMMs exhibit remarkable IQA ability on coarse-grained quality comparison, but there is room for improvement on fine-grained quality discrimination. The proposed dataset sheds light on the future development of IQA models based on LMMs. The codes will be made publicly available at https://github.com/h4nwei/2AFC-LMMs.
https://arxiv.org/abs/2402.01162v1
Given two structures $\mathcal{M}$ and $\mathcal{N}$ on the same domain, we say that $\mathcal{N}$ is a reduct of $\mathcal{M}$ if all $\emptyset$-definable relations of $\mathcal{N}$ are $\emptyset$-definable in $\mathcal{M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are $\aleph_0$-categorical, determining their reducts is equivalent to determining all closed supergroups $G<$ Sym$(\mathbb{N})$ of their automorphism groups. A consequence of the classification is that there are $2^{\aleph_0}$ pairwise non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are $2^{\aleph_0}$ pairwise non-conjugate maximal-closed subgroups of Sym$(\mathbb{N})$. By the reconstruction results of Rubin, these groups are also non-isomorphic as abstract groups.
http://arxiv.org/abs/1509.07674v1
The 2$\alpha+t$ cluster structure in $^{11}$B is investigated by the microscopic generator coordinate method (GCM) with the Brink cluster wave functions. With a proper choice of the parameters of the effective interaction, the calculated energy spectrum shows reasonable agreement with the observed low-lying spectra of both parities. On the basis of the calculated radii, monopole and $B(E2)$ transition strengths, several developed cluster states of $^{11}$B are suggested. For the negative-parity states, in addition to the well-known $3/2_3^-$ cluster state, the $1/2_2^-$ and $5/2_3^-$ states are also proposed as the well-developed cluster states. For the positive-parity states, it is found that many states around the 2$\alpha+t$ threshold show the feature of developed clusters. In particular, the $1/2_2^+$ state is found to have a linear-chain-like structure, which is consistent with the previous antisymmetrized molecular dynamics calculation, but contradicts to the orthogonality condition model calculation. It is also found that many of these positive-parity cluster candidates have the non-negligible isoscalar dipole transition strengths, which require the experimental confirmation.
http://arxiv.org/abs/1711.04439v1
Equiangular tight frames (ETFs) are configurations of vectors which are optimally geometrically spread apart and provide resolutions of the identity. Many known constructions of ETFs are group covariant, meaning they result from the action of a group on a vector, like all known constructions of symmetric, informationally complete, positive operator-valued measures. In this short article, some results characterizing the transitivity of the symmetry groups of ETFs will be presented as well as a proof that an infinite class of so-called Gabor-Steiner ETFs are roux lines, where roux lines are a generalization of doubly transitive lines.
http://arxiv.org/abs/1901.10612v2
We shall show that 2 and 9 are the only biunitary superperfect numbers.
http://arxiv.org/abs/1705.00189v1
Approximation algorithms for the prize-collecting Steiner forest problem (PCSF) have been a subject of research for over three decades, starting with the seminal works of Agrawal, Klein, and Ravi and Goemans and Williamson on Steiner forest and prize-collecting problems. In this paper, we propose and analyze a natural deterministic algorithm for PCSF that achieves a $2$-approximate solution in polynomial time. This represents a significant improvement compared to the previously best known algorithm with a $2.54$-approximation factor developed by Hajiaghayi and Jain in 2006. Furthermore, K{\"{o}}nemann, Olver, Pashkovich, Ravi, Swamy, and Vygen have established an integrality gap of at least $9/4$ for the natural LP relaxation for PCSF. However, we surpass this gap through the utilization of a combinatorial algorithm and a novel analysis technique. Since $2$ is the best known approximation guarantee for Steiner forest problem, which is a special case of PCSF, our result matches this factor and closes the gap between the Steiner forest problem and its generalized version, PCSF.
https://arxiv.org/abs/2309.05172v2
An interesting fact is that most of the known connected $2$-arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are $(\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$. This motivates the study of $2$-arc-transitive Cayley graphs on $\mathrm{A}_n$ for arbitrary valency. In this paper, we characterize the automorphism groups of such graphs. In particular, we show that for a non-complete $(G,2)$-arc-transitive Cayley graph on $\mathrm{A}_n$ with $G$ almost simple, the socle of $G$ is either $\mathrm{A}_{n+1}$ or $\mathrm{A}_{n+2}$. We also construct the first infinite family of $(\mathrm{A}_{n+2},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$.
https://arxiv.org/abs/2103.14784v1
For any $r\geq 1$ and $\mathbf{n} \in \mathbb{Z}_{\geq0}^r \setminus \{\mathbf0\}$ we construct a poset $W_{\mathbf{n}}$ called a 2-associahedron. The 2-associahedra arose in symplectic geometry, where they are expected to control maps between Fukaya categories of different symplectic manifolds. We prove that the completion $\widehat{W_{\mathbf{n}}}$ is an abstract polytope of dimension $|\mathbf{n}|+r-3$. There are forgetful maps $W_{\mathbf{n}} \to K_r$, where $K_r$ is the $(r-2)$-dimensional associahedron, and the 2-associahedra specialize to the associahedra (in two ways) and to the multiplihedra. In an appendix, we work out the 2- and 3-dimensional associahedra in detail.
http://arxiv.org/abs/1709.00119v2
We use Majorana representations to study the subalgebras of the Griess algebra that have shape $(2B,3A,5A)$ and whose associated Miyamoto groups are isomorphic to $A_n$. We prove that these subalgebras exist only if $n\in \{5,6,8\}$. The case $n=5$ was already treated by Ivanov, Seress, McInroy, and Shpectorov. In case $n=6$ we prove that these algebras are all isomorphic and provide their precise description. In case $n=8$ we prove that these algebras do not arise from standard Majorana representations.
https://arxiv.org/abs/2504.17446v1
In this paper, we tackle the classification of gender in facial images with deep learning. Our convolutional neural networks (CNN) use the VGG-16 architecture [1] and are pretrained on ImageNet for image classification. Our proposed method (2^B3^C) first detects the face in the facial image, increases the margin of a detected face by 50%, cropping the face with two boxes three crop schemes (Left, Middle, and Right crop) and extracts the CNN predictions on the cropped schemes. The CNNs of our method is fine-tuned on the Adience and LFW with gender annotations. We show the effectiveness of our method by achieving 90.8% classification on Adience and achieving competitive 95.3% classification accuracy on LFW dataset. In addition, to check the true ability of our method, our gender classification system has a frame rate of 7-10 fps (frames per seconds) on a GPU considering real-time scenarios.
http://arxiv.org/abs/1803.02181v1
We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any given letter frequencies. We provide an upper bound on factor and abelian complexity of these sequences. Using the interpretation by rectangle exchange transformation, we prove that for almost all triples of letter frequencies, the upper bound on factor and abelian complexity is reached. The bound on factor complexity is given using a number-theoretical function which we compute explicitly for a class of parameters.
https://arxiv.org/abs/2403.12791v1
Large speech models are rapidly gaining traction in research community. As a result, model compression has become an important topic, so that these models can fit in memory and be served with reduced cost. Practical approaches for compressing automatic speech recognition (ASR) model use int8 or int4 weight quantization. In this study, we propose to develop 2-bit ASR models. We explore the impact of symmetric and asymmetric quantization combined with sub-channel quantization and clipping on both LibriSpeech dataset and large-scale training data. We obtain a lossless 2-bit Conformer model with 32% model size reduction when compared to state of the art 4-bit Conformer model for LibriSpeech. With the large-scale training data, we obtain a 2-bit Conformer model with over 40% model size reduction against the 4-bit version at the cost of 17% relative word error rate degradation
https://arxiv.org/abs/2305.16619v1
Image retrieval utilizes image descriptors to retrieve the most similar images to a given query image. Convolutional neural network (CNN) is becoming the dominant approach to extract image descriptors for image retrieval. For low-power hardware implementation of image retrieval, the drawback of CNN-based feature descriptor is that it requires hundreds of megabytes of storage. To address this problem, this paper applies deep model quantization and compression to CNN in ASIC chip for image retrieval. It is demonstrated that the CNN-based features descriptor can be extracted using as few as 2-bit weights quantization to deliver a similar performance as floating-point model for image retrieval. In addition, to implement CNN in ASIC, especially for large scale images, the limited buffer size of chips should be considered. To retrieve large scale images, we propose an improved pooling strategy, region nested invariance pooling (RNIP), which uses cropped sub-images for CNN. Testing results on chip show that integrating RNIP with the proposed 2-bit CNN model compression approach is capable of retrieving large scale images.
https://arxiv.org/abs/1905.03362v1
The method of random projections has become a standard tool for machine learning, data mining, and search with massive data at Web scale. The effective use of random projections requires efficient coding schemes for quantizing (real-valued) projected data into integers. In this paper, we focus on a simple 2-bit coding scheme. In particular, we develop accurate nonlinear estimators of data similarity based on the 2-bit strategy. This work will have important practical applications. For example, in the task of near neighbor search, a crucial step (often called re-ranking) is to compute or estimate data similarities once a set of candidate data points have been identified by hash table techniques. This re-ranking step can take advantage of the proposed coding scheme and estimator. As a related task, in this paper, we also study a simple uniform quantization scheme for the purpose of building hash tables with projected data. Our analysis shows that typically only a small number of bits are needed. For example, when the target similarity level is high, 2 or 3 bits might be sufficient. When the target similarity level is not so high, it is preferable to use only 1 or 2 bits. Therefore, a 2-bit scheme appears to be overall a good choice for the task of sublinear time approximate near neighbor search via hash tables. Combining these results, we conclude that 2-bit random projections should be recommended for approximate near neighbor search and similarity estimation. Extensive experimental results are provided.
http://arxiv.org/abs/1602.06577v1
Valley degree of freedom, an excellent information carrier in valleytronics, has been further introduced into advanced microstructure systems for achieving the acoustic valley-Hall topological insulators (VHTIs), which host valley-projected edge states suppressing the undesired sound backscattering under certain perturbations. Therein, the majority of previous literatures focused on single frequency region, and the lack of capability of simultaneous multi-band operation with individual control radically impedes their potential applications. Here, a binary topological-encoded acoustic VHTI is investigated both theoretically and experimentally to manipulate each of the dual-band valley-projected edge states. Through arranging different coding elements derived from the combined valley-Chern numbers, the existence and propagation directions of the frequency selective edge states can be configured in corresponding frequency regions individually. On this basis, three types of proof-of-concept acoustic topological-encoded functional devices are designed, including frequency beam splitter, anti-interference demultiplex topological sensing and composite topological whispering gallery. Our proposal may provide versatile possibilities for achieving the integrated multifunctional systems in multi-channel signal processing and memorizing with high efficiency and high capacity.
https://arxiv.org/abs/2104.10607v3
Recently, with the growing popularity of mobile devices as well as video sharing platforms (e.g., YouTube, Facebook, TikTok, and Twitch), User-Generated Content (UGC) videos have become increasingly common and now account for a large portion of multimedia traffic on the internet. Unlike professionally generated videos produced by filmmakers and videographers, typically, UGC videos contain multiple authentic distortions, generally introduced during capture and processing by naive users. Quality prediction of UGC videos is of paramount importance to optimize and monitor their processing in hosting platforms, such as their coding, transcoding, and streaming. However, blind quality prediction of UGC is quite challenging because the degradations of UGC videos are unknown and very diverse, in addition to the unavailability of pristine reference. Therefore, in this paper, we propose an accurate and efficient Blind Video Quality Assessment (BVQA) model for UGC videos, which we name 2BiVQA for double Bi-LSTM Video Quality Assessment. 2BiVQA metric consists of three main blocks, including a pre-trained Convolutional Neural Network (CNN) to extract discriminative features from image patches, which are then fed into two Recurrent Neural Networks (RNNs) for spatial and temporal pooling. Specifically, we use two Bi-directional Long Short Term Memory (Bi-LSTM) networks, the first is used to capture short-range dependencies between image patches, while the second allows capturing longrange dependencies between frames to account for the temporal memory effect. Experimental results on recent large-scale UGC VQA datasets show that 2BiVQA achieves high performance at lower computational cost than most state-of-the-art VQA models. The source code of our 2BiVQA metric is made publicly available at: https://github.com/atelili/2BiVQA
https://arxiv.org/abs/2208.14774v3
A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. A strongly biconnected component of a strongly connected graph $G=(V,E)$ is a maximal vertex subset $L\subseteq V$ such that the induced subgraph on $L$ is strongly biconnected. Let $G=(V,E)$ be a strongly biconnected directed graph. A $2$-edge-biconnected block in $G$ is a maximal vertex subset $U\subseteq V$ such that for any two distict vertices $v,w \in U$ and for each edge $b\in E$, the vertices $v,w$ are in the same strongly biconnected components of $G\setminus\left\lbrace b\right\rbrace $. A $2$-strong-biconnected block in $G$ is a maximal vertex subset $U\subseteq V$ of size at least $2$ such that for every pair of distinct vertices $v,w\in U$ and for every vertex $z\in V\setminus\left\lbrace v,w \right\rbrace $, the vertices $v$ and $w$ are in the same strongly biconnected component of $G\setminus \left\lbrace v,w \right\rbrace $. In this paper we study $2$-edge-biconnected blocks and $2$-strong biconnected blocks.
http://arxiv.org/abs/2007.09793v1
We study blocks with an abelian defect group and a cyclic inertial quotient acting freely but not transitively. We prove that when p=2, such blocks are inertial, i.e. basic Morita equivalent to their Brauer correspondent. Together with a result of the second author on Singer cycle actions on homocyclic defect groups, this completes the classification of 2-blocks with a cyclic inertial quotient acting freely on an abelian defect group.
http://arxiv.org/abs/2010.08329v2
Semi-visible jets arise in strongly interacting dark sector, resulting in jets overlapping with the missing transverse momentum direction. The implementation of semi-visible jets is done using the Pythia Hidden Valley module to mimic the QCD sector showering in so-called dark shower. In this work, only heavy flavour Standard Model quarks are considered in dark shower, resulting in a much less ambiguous collider signature of semi-visible jets compared to the democratic production of all five quark flavours in dark shower. The constraints from available searches on this signature are presented, and it is shown the signal reconstruction can be improved by using variable-radius jets. Finally a search strategy is suggested.
https://arxiv.org/abs/2207.01885v4
Motivated by new physics models which lead to final states containing a high multiplicity of bottom and top quarks, we develop a tagging strategy to suppress reducible and non-reducible multi-jet backgrounds. The idea takes advantage of the properties of light parton showers and of the gluon fragmentation into heavy quarks to reject jets that do not originate from a bottom quark.
https://arxiv.org/abs/2310.04380v2
As Deep Neural Networks (DNNs) grow in size and complexity, they often exceed the memory capacity of a single accelerator, necessitating the sharding of model parameters across multiple accelerators. Pipeline parallelism is a commonly used sharding strategy for training large DNNs. However, current implementations of pipeline parallelism are being unintentionally bottlenecked by the automatic differentiation tools provided by ML frameworks. This paper introduces 2-stage backpropagation (2BP). By splitting the backward propagation step into two separate stages, we can reduce idle compute time. We tested 2BP on various model architectures and pipelining schedules, achieving increases in throughput in all cases. Using 2BP, we were able to achieve a 1.70x increase in throughput compared to traditional methods when training a LLaMa-like transformer with 7 billion parameters across 4 GPUs.
https://arxiv.org/abs/2405.18047v1
We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressible fluids has an unsuspected relation with minimal supergravity in seven dimensions. We show that just D=7 supergravity and no other theory with the same field content but different coefficients in the lagrangian, admits exact two-brane solutions where Arnold-Beltrami fluxes in the transverse directions have been switched on. The rich variety of discrete groups that classify the solutions of Beltrami equation, namely the eigenfunctions of the *d operator on a three-torus, are by this newly discovered token injected into the brane world. A new quite extensive playing ground opens up for supergravity and for its dual gauge theories in three dimensions, where all classical fields and all quantum composite operators will be assigned to irreducible representations of discrete crystallographic groups.
http://arxiv.org/abs/1504.06802v1
This paper presents a simple yet effective approach for the poorly investigated task of global action segmentation, aiming at grouping frames capturing the same action across videos of different activities. Unlike the case of videos depicting all the same activity, the temporal order of actions is not roughly shared among all videos, making the task even more challenging. We propose to use activity labels to learn, in a weakly-supervised fashion, action representations suitable for global action segmentation. For this purpose, we introduce a triadic learning approach for video pairs, to ensure intra-video action discrimination, as well as inter-video and inter-activity action association. For the backbone architecture, we use a Siamese network based on sparse transformers that takes as input video pairs and determine whether they belong to the same activity. The proposed approach is validated on two challenging benchmark datasets: Breakfast and YouTube Instructions, outperforming state-of-the-art methods.
https://arxiv.org/abs/2412.12829v1
As a generalization of acyclic 2-Calabi-Yau categories, we consider 2-Calabi-Yau categories with a directed cluster-tilting subcategory; we study their cluster-tilting subcategories and the cluster combinatorics that they encode. We show that such categories have a cluster structure. Triangulated 2-Calabi-Yau categories with a directed cluster-tilting subcategory are closely related to representations of certain semi-hereditary categories, more specifically to representations of thread quivers. Thread quivers are a tool to classify and study certain semi-hereditary categories using both quivers and linearly ordered sets (threads). We study the case where the thread quiver consists of a single thread (so that representations of this thread quiver correspond to representations of some linearly ordered set), and show that, similar to the case of a Dynkin quiver of type $A$, the cluster-tilting subcategories can be understood via triangulations of an associated cyclically ordered set. In this way, we gain insight into the structure of the cluster-tilting subcategories of 2-Calabi-Yau categories with a directed cluster-tilting subcategory. As an application, we show that every 2-Calabi-Yau category which admits a directed cluster-tilting subcategory with countably many isomorphism classes of indecomposable objects has a cluster-tilting subcategory $\mathcal{V}$ with the following property: any rigid object in the cluster category can be reached from $\mathcal{V}$ by finitely many mutations. This implies that there is a cluster map which is defined on all rigid objects, and thus that there is a cluster algebra whose cluster variables are exactly given by the rigid indecomposable objects.
http://arxiv.org/abs/1611.03836v1
In this paper, we provide a notion of $\infty$-bicategories fibred in $\infty$-bicategories which we call 2-Cartesian fibrations. Our definition is formulated using the language of marked biscaled simplicial sets: Those are scaled simplicial sets equipped with an additional collection of triangles containing the scaled 2-simplices, which we call lean triangles, in addition to a collection of edges containing all degenerate 1-simplices. We prove the existence of a left proper combinatorial simplicial model category whose fibrant objects are precisely the 2-Cartesian fibrations over a chosen scaled simplicial set $S$. Over the terminal scaled simplicial set, this provides a new model structure modeling $\infty$-bicategories, which we show is Quillen equivalent to Lurie's scaled simplicial set model. We conclude by providing a characterization of 2-Cartesian fibrations over an $\infty$-bicategory. This characterization then allows us to identify those 2-Cartesian fibrations arising as the coherent nerve of a fibration of $\operatorname{Set}^+_{\Delta}$-enriched categories, thus showing that our definition recovers the preexisting notions of fibred 2-categories.
https://arxiv.org/abs/2106.03606v1
In this work, we conclude our study of fibred $\infty$-bicategories by providing a Grothendieck construction in this setting. Given a scaled simplicial set $S$ (which need not be fibrant) we construct a 2-categorical version of Lurie's straightening-unstraightening adjunction, thereby furnishing an equivalence between the $\infty$-bicategory of 2-Cartesian fibrations over $S$ and the $\infty$-bicategory of contravariant functors $S^{\operatorname{op}} \to \mathbb{B}\mathbf{\!}\operatorname{icat}_\infty$ with values in the $\infty$-bicategory of $\infty$-bicategories. We provide a relative nerve construction in the case where the base is a 2-category, and use this to prove a comparison to existing bicategorical Grothendieck constructions.
https://arxiv.org/abs/2201.09589v3
We produce 2-representations of the positive part of affine quantum enveloping algebras on their finite-dimensional counterparts in type $A_n$. These 2-representations naturally extend the right-multiplication 2-representation of $U_q^+(\mathfrak{sl}_{n+1})$ on itself and are closely related to evaluation morphisms of quantum groups. We expect that our 2-representation exists in all simple types and show that the corresponding 1-representation exists in type $D_4$.
https://arxiv.org/abs/2502.08039v2
Throughout this paper $G$ is a fixed group, and $k$ is a fixed field. All categories are assumed to be $k$-linear. First we give a systematic way to induce $G$-precoverings by adjoint functors using a 2-categorical machinery, which unifies many similar constructions of $G$-precoverings. Now let $\mathcal{C}$ be a skeletally small category with a $G$-action, $\mathcal{C}/G$ the orbit category of $\mathcal{C}$, $(P, \phi) : \mathcal{C} \rightarrow \mathcal{C}/G$ the canonical $G$-covering, and $\mathrm{mod}\mbox{-} \mathcal{C}$, $\mathrm{mod}\mbox{-} (\mathcal{C}/G)$ the categories of finitely generated modules over $\mathcal{C}, \mathcal{C}/G$, respectively. Then it is well known that there exists a canonical G-precovering $(P., \phi.) : \mathrm{mod}\mbox{-} \mathcal{C} \rightarrow \mathrm{mod}\mbox{-} (\mathcal{C}/G)$. By applying the machinery above to this $(P., \phi.)$, new $G$-precoverings $(\mathrm{mod}\mbox{-} \mathcal{C}) / S \rightarrow (\mathrm{mod}\mbox{-} \mathcal{C}/G)/S'$ are induced between the factor categories or localizations of $\mathrm{mod}\mbox{-} \mathcal{C}$ and $\mathrm{mod}\mbox{-} \mathcal{C}/G$, respectively. This is further applied to the morphism category $\mathrm{H}(\mathrm{mod}\mbox{-} \mathcal{C})$ of $\mathrm{mod}\mbox{-} \mathcal{C}$ to have a $G$-precovering $\mathrm{fp}(\mathcal{K}) \rightarrow \mathrm{fp}(\mathcal{K}')$ between the categories of finitely presented modules over suitable subcategories $\mathcal{K}$ and $\mathcal{K}'$ of $\mathrm{mod}\mbox{-}\mathcal{C}$ and $ \mathrm{mod}\mbox{-} \mathcal{C}/G$, respectively.
https://arxiv.org/abs/2402.04680v1
In this paper we show that the strict and lax pullbacks of a 2-categorical opfibration along an arbitrary 2-functor are homotopy equivalent. We give two applications. First, we show that the strict fibers of an opfibration model the homotopy fibers. This is a version of Quillen's Theorem B amenable to applications. Second, we compute the $E^2$ page of a homology spectral sequence associated to an opfibration and apply this machinery to a 2-categorical construction of $S^{-1}S$. We show that if $S$ is a symmetric monoidal 2-groupoid with faithful translations then $S^{-1}S$ models the group completion of $S$.
https://arxiv.org/abs/2010.11173v2
The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of Connes and Moscovici arises from a distributive law, and to clarify the role of different notions of bimonad in this generalisation. 2) To extend the procedure of twisting the cyclic homology of a unital associative algebra to any duplicial object defined by a distributive law. 3) To study the universality of Bohm and Stefan's approach to constructing duplicial objects, which we do in terms of a 2-categorical generalisation of Hochschild (co)homology. 4) To characterise those categories whose nerve admits a duplicial structure.
http://arxiv.org/abs/1605.08992v1
In this paper we present $2$-category theory from the perspective of Gray-categories using the graphical calculus of separated surface diagrams. As an extended example we consider cones and limits of $2$-functors. Then we use the canonical adjunction between $2$-computads and $2$-categories to interpret the comparison structure of lax functors and extend the surface diagram calculus with compositor sheets in order to represent and reason about them.
https://arxiv.org/abs/2203.08783v1
In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting $2$-category is fiat (in the sense of \cite{MM1}) and classify simple transitive $2$-representations of this $2$-category (under some mild technical assumption). We also study several classes of examples in detail.
http://arxiv.org/abs/1904.05798v1
In that paper, we prove that the collection of all FRBSU monoidal categories and the collection of all crossed modules form a 2 category.
http://arxiv.org/abs/1512.06981v1
Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of Hilb. In this paper, we argue that a categorical formalism that captures and unifies both anyonic theories (the Hardware of quantum computing) and a model of topological quantum computing is a braided (fusion) 2-category. In this 2-category, 0-morphisms describe anyonic types and Hom-categories describe different models of quantum computing. This picture provides an insightful perspective on superselection rules. It presents furthermore a clear distinction between fusion of anyons versus tensor products as defined in linear algebra, between vector spaces of 1-morphisms. The former represents a monoidal product and sum between 0-morphisms and the latter a tensor product and direct sum between 1-morphisms.
https://arxiv.org/abs/2505.22171v1
Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single copulating function, $C$, that links these marginals. For bivariate data, a copula takes the form of a two-increasing function $C: (u,v)\in \mathbb{I}^2 \rightarrow \mathbb{I}$, where $\mathbb{I} = [0, 1]$. This paper proposes 2-Cats, a Neural Network (NN) model that learns two-dimensional Copulas without relying on specific Copula families (e.g., Archimedean). Furthermore, via both theoretical properties of the model and a Lagrangian training approach, we show that 2-Cats meets the desiderata of Copula properties. Moreover, inspired by the literature on Physics-Informed Neural Networks and Sobolev Training, we further extend our training strategy to learn not only the output of a Copula but also its derivatives. Our proposed method exhibits superior performance compared to the state-of-the-art across various datasets while respecting (provably for most and approximately for a single other) properties of C.
https://arxiv.org/abs/2309.16391v5
To achieve sub-picometer sensitivities in the millihertz band, laser interferometric inertial sensors rely on some form of reduction of the laser frequency noise, typically by locking the laser to a stable frequency reference, such as the narrow-linewidth resonance of an ultra-stable optical cavity or an atomic or molecular transition. In this paper we report on a compact laser frequency stabilization technique based on an unequal-arm Mach-Zehnder interferometer that is sub-nanometer stable at $10\,\mu$Hz, sub-picometer at $0.5\,$mHz, and reaches a noise floor of $7\,\mathrm{fm}/\!\sqrt{\mathrm{Hz}}$ at 1 Hz. The interferometer is used in conjunction with a DC servo to stabilize the frequency of a laser down to a fractional instability below $4 \times 10^{-13}$ at averaging times from 0.1 to 100 seconds. The technique offers a wide operating range, does not rely on complex lock acquisition procedures, and can be readily integrated as part of the optical bench in future gravity missions.
https://arxiv.org/abs/2308.11325v2
Recent studies have used GAN to transfer expressions between human faces. However, existing models have many flaws: relying on emotion labels, lacking continuous expressions, and failing to capture the expression details. To address these limitations, we propose a novel CycleGAN- and InfoGAN-based network called 2 Cycles Expression Transfer GAN (2CET-GAN), which can learn continuous expression transfer without using emotion labels. The experiment shows our network can generate diverse and high-quality expressions and can generalize to unknown identities. To the best of our knowledge, we are among the first to successfully use an unsupervised approach to disentangle expression representation from identities at the pixel level.
https://arxiv.org/abs/2211.11570v1
We introduce a new family of finite posets which we call 2-chains. These first arose in the study of 0-Hecke algebras, but they admit a variety of different characterisations. We give these characterisations, prove that they are equivalent and derive some numerical results concerning 2-chains.
http://arxiv.org/abs/1809.07574v2
We perform a detailed study of perturbations around 2-charge circular fuzz-balls and compare the results with the ones obtained in the case of 'small' BHs. In addition to the photon-sphere modes that govern the prompt ring-down, we find a new branch of long-lived QNMs localised inside the photon-sphere at the (meta)stable minimum of the radial effective potential. The latter are expected to dominate late time signals in the form of 'echoes'. Moreover, contrary to 'small' BHs, some 'static' tidal Love numbers are non-zero and independent of the mass, charges and angular momentum of the fuzz-ball. We rely on the recently established connection between BH or fuzz-ball perturbation theory and quantum Seiberg-Witten curves for N = 2 SYM theories, which in turn are related to Liouville CFT via the AGT correspondence. We test our results against numerical results obtained with Leaver's method of continuous fractions or Breit-Wigner resonance method for direct integration and with the WKB approximation based on geodesic motion. We also exclude rotational super-radiance, due to the absence of an ergo-region, and absorption, due to the absence of a horizon.
https://arxiv.org/abs/2212.07504v1
Let $d$ be a positive square-free integer. In this paper we shall investigate the structure of the $2$-class group of the cyclotomic $\mathbb{Z}_2$-extension of the imaginary biquadratic number field $\mathbb{Q}(\sqrt{d},\sqrt{-1})$. Furthermore, we deduce the structure of the $2$-class group of cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{-d})$.
http://arxiv.org/abs/2002.03602v3
We expand the theory of 2-classifiers, that are a 2-categorical generalization of subobject classifiers introduced by Weber. The idea is to upgrade monomorphisms to discrete opfibrations. We prove that the conditions of 2-classifier can be checked just on a dense generator. The study of what is classified by a 2-classifier is similarly reduced to a study over the objects that form a dense generator. We then apply our results to the cases of prestacks and stacks, where we can thus look just at the representables. We produce a 2-classifier in prestacks that classifies all discrete opfibrations with small fibres. Finally, we restrict such 2-classifier to a 2-classifier in stacks. This is the main ingredient of a proof that Grothendieck 2-topoi are elementary 2-topoi. Our results also solve a problem posed by Hofmann and Streicher when attempting to lift Grothendieck universes to sheaves.
https://arxiv.org/abs/2401.16900v3
We show that 2-CLUB is NP-hard for distance to 2-club cluster graphs.
http://arxiv.org/abs/1903.05425v1
We reduce the dynamics of an ensemble of mean-coupled Stuart-Landau oscillators close to the synchronized solution. In particular, we map the system onto the center manifold of the Benjamin-Feir instability, the bifurcation destabilizing the synchronized oscillation. Using symmetry arguments, we describe the structure of the dynamics on this center manifold up to cubic order, and derive expressions for its parameters. This allows us to investigate phenomena described by the Stuart-Landau ensemble, such as clustering and cluster singularities, in the lower-dimensional center manifold, providing further insights into the symmetry-broken dynamics of coupled oscillators. We show that cluster singularities in the Stuart-Landau ensemble correspond to vanishing quadratic terms in the center manifold dynamics. In addition, they act as organizing centers for the saddle-node bifurcations creating unbalanced cluster states as well for the transverse bifurcations altering the cluster stability. Furthermore, we show that bistability of different solutions with the same cluster-size distribution can only occur when either cluster contains at least $1/3$ of the oscillators, independent of the system parameters.
https://arxiv.org/abs/2010.06221v2
This paper introduces an innovative approach for handling 2D compound hypotheses within the Belief Function Theory framework. We propose a polygon-based generic rep- resentation which relies on polygon clipping operators. This approach allows us to account in the computational cost for the precision of the representation independently of the cardinality of the discernment frame. For the BBA combination and decision making, we propose efficient algorithms which rely on hashes for fast lookup, and on a topological ordering of the focal elements within a directed acyclic graph encoding their interconnections. Additionally, an implementation of the functionalities proposed in this paper is provided as an open source library. Experimental results on a pedestrian localization problem are reported. The experiments show that the solution is accurate and that it fully benefits from the scalability of the 2D search space granularity provided by our representation.
http://arxiv.org/abs/1803.08857v1
In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of $n$-coherent and $n$-convex conditional previsions, at the varying of $n$. We investigate which such previsions are the most general one may reasonably consider, suggesting (centered) $2$-convex or, if positive homogeneity and conjugacy is needed, $2$-coherent lower previsions. Basic properties of these previsions are studied. In particular, we prove that they satisfy the Generalized Bayes Rule and always have a $2$-convex or, respectively, $2$-coherent natural extension. The role of these extensions is analogous to that of the natural extension for coherent lower previsions. On the contrary, $n$-convex and $n$-coherent previsions with $n\geq 3$ either are convex or coherent themselves or have no extension of the same type on large enough sets. Among the uncertainty concepts that can be modelled by $2$-convexity, we discuss generalizations of capacities and niveloids to a conditional framework and show that the well-known risk measure Value-at-Risk only guarantees to be centered $2$-convex. In the final part, we determine the rationality requirements of $2$-convexity and $2$-coherence from a desirability perspective, emphasising how they weaken those of (Williams) coherence.
http://arxiv.org/abs/1606.06043v1
The program of internal type theory seeks to develop the categorical model theory of dependent type theory using the language of dependent type theory itself. In the present work we study internal homotopical type theory by relaxing the notion of a category with families (cwf) to that of a wild, or precoherent higher cwf, and determine coherence conditions that suffice to recover properties expected of models of dependent type theory. The result is a definition of a split 2-coherent wild cwf, which admits as instances both the syntax and the "standard model" given by a universe type. This allows us to give a straightforward internalization of the notion of a 2-coherent reflection of homotopical type theory in itself: namely as a 2-coherent wild cwf morphism from the syntax to the standard model. Our theory also easily specializes to give definitions of "low-dimensional" higher cwfs, and conjecturally includes the container higher model as a further instance.
https://arxiv.org/abs/2503.05790v1
We characterize noncommutative symmetric Banach spaces for which every bounded sequence admits either a convergent subsequence, or a $2$-co-lacunary subsequence. This extends the classical characterization, due to R\"abiger.
http://arxiv.org/abs/1909.04258v1
The 2-colorable perfect matching problem asks whether a graph can be colored with two colors so that each node has exactly one neighbor with the same color as itself. We prove that this problem is NP-complete, even when restricted to 2-connected 3-regular planar graphs. In 1978, Schaefer proved that this problem is NP-complete in general graphs, and claimed without proof that the same result holds when restricted to 3-regular planar graphs. Thus we fill in the missing proof of this claim, while simultaneously strengthening to 2-connected graphs (which implies existence of a perfect matching). We also prove NP-completeness of $k$-colorable perfect matching, for any fixed $k \geq 2$.
https://arxiv.org/abs/2309.09786v1
In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some Overpartition identities coincide with our findings. A correspondence between colored partitions and overpartitions is provided.
https://arxiv.org/abs/2203.15378v1
The 2-girth of a 2-dimensional simplicial complex $X$ is the minimum size of a non-zero 2-cycle in $H_2(X, \mathbb{Z}/2)$. We consider the maximum possible girth of a complex with $n$ vertices and $m$ 2-faces. If $m = n^{2 + \alpha}$ for $\alpha < 1/2$, then we show that the 2-girth is at most $4 n^{2 - 2 \alpha}$ and we prove the existence of complexes with 2-girth at least $c_{\alpha, \epsilon} n^{2 - 2 \alpha - \epsilon}$. On the other hand, if $\alpha > 1/2$, the 2-girth is at most $C_{\alpha}$. So there is a phase transition as $\alpha$ passes 1/2. Our results depend on a new upper bound for the number of combinatorial types of triangulated surfaces with $v$ vertices and $f$ faces.
http://arxiv.org/abs/1509.03871v2
A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected $2$-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem.
https://arxiv.org/abs/2109.04085v1
In this paper, we study 2-complex symmetric composition operators with the conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the necessary and sufficient condition for the composition operator $C_\phi$ to be 2-complex symmetric when the symbols $\phi$ is an automorphism of $\mathbb D$. We also characterize the 2-complex symmetric composition operator $C_\phi$ on the Hardy space $H^2$ when $\phi$ is a linear fractional self-map of $\mathbb D$.
https://arxiv.org/abs/2110.11184v1
A cycle $C$ of length $k$ in graph $G$ is extendable if there is another cycle $C'$ in $G$ with $V(C) \subset V(C')$ and length $k+1$. A graph is cycle extendable if every non-Hamiltonian cycle is extendable. In 1990 Hendry conjectured that any Hamiltonian chordal graph (a Hamiltonian graph with no induced cycle of length greater than three) is cycle extendable, and this conjecture has been verified for Hamiltonian chordal graphs which are interval graphs, planar graphs, and split graphs. We prove that any 2-connected claw-free chordal graph is cycle extendable.
http://arxiv.org/abs/1310.2901v4
Let $G$ be a graph. A total dominating set in a graph $G$ is a set $S$ of vertices of $G$ such that every vertex in $G$ is adjacent to a vertex in $S$. Recently, the following question was proposed: "Is it true that every connected cubic graph containing a $3$-cycle has two vertex disjoint total dominating sets?" In this paper, we give a negative answer to this question. Moreover, we prove that if we replace $3$-cycle with $4$-cycle the answer is affirmative. This implies every connected cubic graph containing a diamond (the complete graph of order $4$ minus one edge) as a subgraph can be partitioned into two total dominating sets, a result that was proved in 2017.
https://arxiv.org/abs/2308.15114v1
A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is filled injectively with the numbers $1, \ldots ,a_i$, where $a_i$ is the length of $i$th row of $Y$, and every column is also filled injectively. A conjecture of Chow and Taylor, publicized by Chow, Fan, Goemans, and Vondrak is that a wide Young diagram is Latin. We prove a dual version of the conjecture.
https://arxiv.org/abs/2311.17670v2
Federated Learning harnesses data from multiple sources to build a single model. While the initial model might belong solely to the actor bringing it to the network for training, determining the ownership of the trained model resulting from Federated Learning remains an open question. In this paper we explore how Blockchains (in particular Ethereum) can be used to determine the evolving ownership of a model trained with Federated Learning. Firstly, we use the step-by-step evaluation metric to assess the relative contributivities of participants in a Federated Learning process. Next, we introduce 2CP, a framework comprising two novel protocols for Blockchained Federated Learning, which both reward contributors with shares in the final model based on their relative contributivity. The Crowdsource Protocol allows an actor to bring a model forward for training, and use their own data to evaluate the contributions made to it. Potential trainers are guaranteed a fair share of the resulting model, even in a trustless setting. The Consortium Protocol gives trainers the same guarantee even when no party owns the initial model and no evaluator is available. We conduct experiments with the MNIST dataset that reveal sound contributivity scores resulting from both Protocols by rewarding larger datasets with greater shares in the model. Our experiments also showed the necessity to pair 2CP with a robust model aggregation mechanism to discard low quality inputs coming from model poisoning attacks.
https://arxiv.org/abs/2011.07516v1
Let F(X_d) be a smooth Fano variety of lines of a hypersurface X_d of degree d. In this paper, we prove the Griffiths group Griff_1(F(X_d)) is trivial if the hypersurface X_d is of 2-Fano type. As a result, we give a positive answer to a question of Professor Voisin about the first Griffiths groups of Fano varieties in some cases. Base on this result, we prove that CH_2(X_d)=\mathbb{Z} for a complex smooth $3$-Fano hypersurface X_d whose Fano variety of lines is smooth.
http://arxiv.org/abs/1512.01721v3
We discuss the realization of $2d$ $(0,2)$ gauge theories in terms of branes focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi-Yau 4-folds. These brane setups fully encode the infinite class of $2d$ $(0,2)$ quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. We review various methods for efficiently generating Brane Brick Models. These algorithms are then used to construct $2d$ $(0,2)$ gauge theories for the cones over all the smooth Fano 3-folds and two infinite families of Sasaki-Einstein 7-manifolds with known metrics. This note is based on the author's talk at the Gauged Linear Sigma Models @ 30 conference at the Simons Center for Geometry and Physics.
https://arxiv.org/abs/2402.06993v1
We initiate a systematic study of 2d (0,2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theory. Finally, we introduce Brane Brick Models, a novel class of brane configurations that consist of D4-branes suspended from an NS5-brane wrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are the 2d analogues of Brane Tilings and allow a direct connection between geometry and gauge theory.
http://arxiv.org/abs/1506.03818v2
Relational information between different types of entities is often modelled by a multilayer network (MLN) -- a network with subnetworks represented by layers. The layers of an MLN can be arranged in different ways in a visual representation, however, the impact of the arrangement on the readability of the network is an open question. Therefore, we studied this impact for several commonly occurring tasks related to MLN analysis. Additionally, layer arrangements with a dimensionality beyond 2D, which are common in this scenario, motivate the use of stereoscopic displays. We ran a human subject study utilising a Virtual Reality headset to evaluate 2D, 2.5D, and 3D layer arrangements. The study employs six analysis tasks that cover the spectrum of an MLN task taxonomy, from path finding and pattern identification to comparisons between and across layers. We found no clear overall winner. However, we explore the task-to-arrangement space and derive empirical-based recommendations on the effective use of 2D, 2.5D, and 3D layer arrangements for MLNs.
https://arxiv.org/abs/2307.10674v2
More serious works on 2D2C, 2D3C, 2C2Dcw1C3D, 3D3C, rotating turbulence, thin-layer flows, quasi-static magnetohydrodynamics (QSMHD), and all that are wanted, but we report timely here some studies on locally and globally 2C2Dcw1C3D flows, with the hope to promote smarter and deeper works.
http://arxiv.org/abs/1408.1503v5
We propose a two-factor authentication (2FA) mechanism called 2D-2FA to address security and usability issues in existing methods. 2D-2FA has three distinguishing features: First, after a user enters a username and password on a login terminal, a unique $\textit{identifier}$ is displayed to her. She $\textit{inputs}$ the same identifier on her registered 2FA device, which ensures appropriate engagement in the authentication process. Second, a one-time PIN is computed on the device and $\textit{automatically}$ transferred to the server. Thus, the PIN can have very high entropy, making guessing attacks infeasible. Third, the identifier is also incorporated into the PIN computation, which renders $\textit{concurrent attacks}$ ineffective. Third-party services such as push-notification providers and 2FA service providers, do not need to be trusted for the security of the system. The choice of identifiers depends on the device form factor and the context. Users could choose to draw patterns, capture QR codes, etc. We provide a proof of concept implementation, and evaluate performance, accuracy, and usability of the system. We show that the system offers a lower error rate (about half) and better efficiency (2-3 times faster) compared to the commonly used PIN-2FA. Our study indicates a high level of usability with a SUS of 75, and a high perception of efficiency, security, accuracy, and adoptability.
https://arxiv.org/abs/2110.15872v1
Despite recent advances in facial recognition, there remains a fundamental issue concerning degradations in performance due to substantial perspective (pose) differences between enrollment and query (probe) imagery. Therefore, we propose a novel domain adaptive framework to facilitate improved performances across large discrepancies in pose by enabling image-based (2D) representations to infer properties of inherently pose invariant point cloud (3D) representations. Specifically, our proposed framework achieves better pose invariance by using (1) a shared (joint) attention mapping to emphasize common patterns that are most correlated between 2D facial images and 3D facial data and (2) a joint entropy regularizing loss to promote better consistency$\unicode{x2014}$enhancing correlations among the intersecting 2D and 3D representations$\unicode{x2014}$by leveraging both attention maps. This framework is evaluated on FaceScape and ARL-VTF datasets, where it outperforms competitive methods by achieving profile (90$\unicode{x00b0}$$\unicode{x002b}$) TAR @ 1$\unicode{x0025}$ FAR improvements of at least 7.1$\unicode{x0025}$ and 1.57$\unicode{x0025}$, respectively.
https://arxiv.org/abs/2505.09073v1
Doping of silicon via phosphene exposures alternating with molecular beam epitaxy overgrowth is a path to Si:P substrates for conventional microelectronics and quantum information technologies. The technique also provides a new and well-controlled material for systematic studies of two-dimensional lattices with a half-filled band. We show here that for a dense ($n_s=2.8\times 10^{14}$\,cm$^{-2}$) disordered two-dimensional array of P atoms, the full field angle-dependent magnetostransport is remarkably well described by classic weak localization theory with no corrections due to interaction effects. The two- to three-dimensional cross-over seen upon warming can also be interpreted using scaling concepts, developed for anistropic three-dimensional materials, which work remarkably except when the applied fields are nearly parallel to the conducting planes.
http://arxiv.org/abs/1802.05208v2
Deformable registration of two-dimensional/three-dimensional (2D/3D) images of abdominal organs is a complicated task because the abdominal organs deform significantly and their contours are not detected in two-dimensional X-ray images. We propose a supervised deep learning framework that achieves 2D/3D deformable image registration between 3D volumes and single-viewpoint 2D projected images. The proposed method learns the translation from the target 2D projection images and the initial 3D volume to 3D displacement fields. In experiments, we registered 3D-computed tomography (CT) volumes to digitally reconstructed radiographs generated from abdominal 4D-CT volumes. For validation, we used 4D-CT volumes of 35 cases and confirmed that the 3D-CT volumes reflecting the nonlinear and local respiratory organ displacement were reconstructed. The proposed method demonstrate the compatible performance to the conventional methods with a dice similarity coefficient of 91.6 \% for the liver region and 85.9 \% for the stomach region, while estimating a significantly more accurate CT values.
https://arxiv.org/abs/2212.05445v1
Recent developments in the registration of histology and micro-computed tomography ({\mu}CT) have broadened the perspective of pathological applications such as virtual histology based on {\mu}CT. This topic remains challenging because of the low image quality of soft tissue CT. Additionally, soft tissue samples usually deform during the histology slide preparation, making it difficult to correlate the structures between histology slide and {\mu}CT. In this work, we propose a novel 2D-3D multi-modal deformable image registration method. The method uses a machine learning (ML) based initialization followed by the registration. The registration is finalized by an analytical out-of-plane deformation refinement. The method is evaluated on datasets acquired from tonsil and tumor tissues. {\mu}CTs of both phase-contrast and conventional absorption modalities are investigated. The registration results from the proposed method are compared with those from intensity- and keypoint-based methods. The comparison is conducted using both visual and fiducial-based evaluations. The proposed method demonstrates superior performance compared to the other two methods.
https://arxiv.org/abs/2410.14343v1
In 2D+3D facial expression recognition (FER), existing methods generate multi-view geometry maps to enhance the depth feature representation. However, this may introduce false estimations due to local plane fitting from incomplete point clouds. In this paper, we propose a novel Map Generation technique from the viewpoint of information theory, to boost the slight 3D expression differences from strong personality variations. First, we examine the HDR depth data to extract the discriminative dynamic range $r_{dis}$, and maximize the entropy of $r_{dis}$ to a global optimum. Then, to prevent the large deformation caused by over-enhancement, we introduce a depth distortion constraint and reduce the complexity from $O(KN^2)$ to $O(KN\tau)$. Furthermore, the constrained optimization is modeled as a $K$-edges maximum weight path problem in a directed acyclic graph, and we solve it efficiently via dynamic programming. Finally, we also design an efficient Facial Attention structure to automatically locate subtle discriminative facial parts for multi-scale learning, and train it with a proposed loss function $\mathcal{L}_{FA}$ without any facial landmarks. Experimental results on different datasets show that the proposed method is effective and outperforms the state-of-the-art 2D+3D FER methods in both FER accuracy and the output entropy of the generated maps.
https://arxiv.org/abs/2011.08333v1
In this paper, a novel approach via embedded tensor manifold regularization for 2D+3D facial expression recognition (FERETMR) is proposed. Firstly, 3D tensors are constructed from 2D face images and 3D face shape models to keep the structural information and correlations. To maintain the local structure (geometric information) of 3D tensor samples in the low-dimensional tensors space during the dimensionality reduction, the $\ell_0$-norm of the core tensors and a tensor manifold regularization scheme embedded on core tensors are adopted via a low-rank truncated Tucker decomposition on the generated tensors. As a result, the obtained factor matrices will be used for facial expression classification prediction. To make the resulting tensor optimization more tractable, $\ell_1$-norm surrogate is employed to relax $\ell_0$-norm and hence the resulting tensor optimization problem has a nonsmooth objective function due to the $\ell_1$-norm and orthogonal constraints from the orthogonal Tucker decomposition. To efficiently tackle this tensor optimization problem, we establish the first-order optimality condition in terms of stationary points, and then design a block coordinate descent (BCD) algorithm with convergence analysis and the computational complexity. Numerical results on BU-3DFE database and Bosphorus databases demonstrate the effectiveness of our proposed approach.
https://arxiv.org/abs/2201.12506v1
In this paper, we develop a 2D and 3D segmentation pipelines for fully automated cardiac MR image segmentation using Deep Convolutional Neural Networks (CNN). Our models are trained end-to-end from scratch using the ACD Challenge 2017 dataset comprising of 100 studies, each containing Cardiac MR images in End Diastole and End Systole phase. We show that both our segmentation models achieve near state-of-the-art performance scores in terms of distance metrics and have convincing accuracy in terms of clinical parameters. A comparative analysis is provided by introducing a novel dice loss function and its combination with cross entropy loss. By exploring different network structures and comprehensive experiments, we discuss several key insights to obtain optimal model performance, which also is central to the theme of this challenge.
http://arxiv.org/abs/1707.09813v1
Multi-modal fusion has been proved to help enhance the performance of scene classification tasks. This paper presents a 2D-3D Fusion stage that combines 3D Geometric Features with 2D Texture Features obtained by 2D Convolutional Neural Networks. To get a robust 3D Geometric embedding, a network that uses two novel layers is proposed. The first layer, Multi-Neighbourhood Graph Convolution, aims to learn a more robust geometric descriptor of the scene combining two different neighbourhoods: one in the Euclidean space and the other in the Feature space. The second proposed layer, Nearest Voxel Pooling, improves the performance of the well-known Voxel Pooling. Experimental results, using NYU-Depth-V2 and SUN RGB-D datasets, show that the proposed method outperforms the current state-of-the-art in RGB-D indoor scene classification task.
https://arxiv.org/abs/2009.11154v3