ShantanuT01/DACTYL-Pretraining huggingface dataset:
One of the main sources of error in multi-atlas segmentation propagation approaches comes from the use of atlas databases that are morphologically dissimilar to the target image. In this work, we exploit the segmentation errors associated with poor atlas selection to build a computer aided diagnosis (CAD) system for pathological classification in post-operative dextro-transposition of the great arteries (d-TGA). The proposed approach extracts a set of features, which describe the quality of a segmentation, and introduces them into a logical decision tree that provides the final diagnosis. We have validated our method on a set of 60 whole heart MR images containing healthy cases and two different forms of post-operative d-TGA. The reported overall CAD system accuracy was of 93.33%.
We deal with connected $k$-regular multigraphs of order $n$ that has only three distinct eigenvalues. In this paper, we study the largest possible number of vertices of such a graph for given $k$. For $k=2,3,7$, the Moore graphs are largest. For $k\ne 2,3,7,57$, we show an upper bound $n\leq k^2-k+1$, with equality if and only if there exists a finite projective plane of order $k-1$ that admits a polarity.
Type IIB string theory admits a BPS configuration in which three strings (of different type) meet at a point. Using this three string configuration we construct a string network and study its properties. In particular we prove supersymmetry of this configuration. We also consider string lattices, which can be used to construct BPS states in toroidally compactified string theory.
We explain the origin of the Kondo mirage seen in recent quantum corral Scanning Tunneling Microscope (STM) experiments with a scattering theory of electrons on the surfaces of metals. Our theory combined with experimental data provides the first direct observation of a single Kondo atom phase shift. The Kondo mirage at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the walls of the corral in a manner analagous to the formation of a real image in optics. We demonstrate our theory with direct quantitive comparision to experimental data.
The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back from time to time to its starting node, the mean search time needed to reach another node of the network may be significantly decreased. In other cases, however, resetting is detrimental to search. Using the eigenvalues and eigenvectors of the transition matrix defining the process without resetting, we derive a general criterion for finite networks that establishes when there exists a non-zero resetting probability that minimizes the mean first passage time at a target node. Right at optimality, the coefficient of variation of the first passage time is not unity, unlike in continuous time processes with instantaneous resetting, but above 1 and depends on the minimal mean first passage time. The approach is general and applicable to the study of different discrete-time ergodic Markov processes such as L\'evy flights, where the long-range dynamics is introduced in terms of the fractional Laplacian of the graph. We apply these results to the study of optimal transport on rings and Cayley trees.
We introduce the space of rough paths with Sobolev regularity and the corresponding concept of controlled Sobolev paths. Based on these notions, we study rough path integration and rough differential equations. As main result, we prove that the solution map associated to differential equations driven by rough paths is a locally Lipschitz continuous map on the Sobolev rough path space for any arbitrary low regularity $\alpha$ and integrability $p$ provided $\alpha >1/p$.
We revisit the periodic homogenization of Dirichlet problems for the Laplace operator in perforated domains, and establish a unified proof that works for different regimes of hole-cell ratios, that is the ratio between the scaling factor of the holes and that of the periodic cells. The approach is then made quantitative and it yields correctors and error estimates for vanishing hole-cell ratios. For positive volume fraction of holes, the approach is just the standard oscillating test function method; for vanishing volume fraction of holes, we study asymptotic behaviors of a properly rescaled cell problems and use them to build oscillating test functions. Our method reveals how the different regimes are intrinsically connected through the cell problems and the connection with periodic layer potentials.
Data from the Relativistic Heavy Ion Collider over the last five years has led many to conclude that the medium created is not the expected quark gluon plasma (QGP), but rather a strongly coupled or strongly interacting quark gluon plasma (sQGP). We explore the meaning of this possible paradigm shift and some of the experimental and theoretical arguments that are associated with it. In this proceedings we detail only a small subset of the relevant issues as discussed at the Hot Quarks 2006 workshop.
An Axial Shifted MLP architecture (AS-MLP) is proposed in this paper. Different from MLP-Mixer, where the global spatial feature is encoded for information flow through matrix transposition and one token-mixing MLP, we pay more attention to the local features interaction. By axially shifting channels of the feature map, AS-MLP is able to obtain the information flow from different axial directions, which captures the local dependencies. Such an operation enables us to utilize a pure MLP architecture to achieve the same local receptive field as CNN-like architecture. We can also design the receptive field size and dilation of blocks of AS-MLP, etc, in the same spirit of convolutional neural networks. With the proposed AS-MLP architecture, our model obtains 83.3% Top-1 accuracy with 88M parameters and 15.2 GFLOPs on the ImageNet-1K dataset. Such a simple yet effective architecture outperforms all MLP-based architectures and achieves competitive performance compared to the transformer-based architectures (e.g., Swin Transformer) even with slightly lower FLOPs. In addition, AS-MLP is also the first MLP-based architecture to be applied to the downstream tasks (e.g., object detection and semantic segmentation). The experimental results are also impressive. Our proposed AS-MLP obtains 51.5 mAP on the COCO validation set and 49.5 MS mIoU on the ADE20K dataset, which is competitive compared to the transformer-based architectures. Our AS-MLP establishes a strong baseline of MLP-based architecture. Code is available at https://github.com/svip-lab/AS-MLP.
The article is a slightly extended version of the talk, with the same title, which I gave at the Kinosaki Symposium on Algebraic Geometry in October 2011, and dealing with the classification of complex projective surfaces of general type with vanishing geometric genus, and especially with the moduli spaces of Burniat surfaces.
In this thesis, we construct a half-integral weight multiplier system on the group SU(2,1). In order to do so, we first find a formula for a 2-cocycle representing the double cover of SU(2,1)(k), where k is a local field. For each non-archimedean local field k, we describe how the cocycle splits on a compact open subgroup. The multiplier system is then expressed in terms of the product of the local splittings at each prime.
We consider random directed graphs, and calculate the distribution of the cokernels of their laplacian, following the methods used by Wood. As a corollary, we show that the probability that a random digraph is coeulerian is asymptotically upper bounded by a constant around $0.43$.
Most galactic nuclei harbor a massive black hole (MBH), whose birth and evolution are closely linked to those of its host galaxy. The unique conditions near the MBH: high velocity and density in the steep potential of a massive singular relativistic object, lead to unusual modes of stellar birth, evolution, dynamics and death. A complex network of dynamical mechanisms, operating on multiple timescales, deflect stars to orbits that intercept the MBH. Such close encounters lead to energetic interactions with observable signatures and consequences for the evolution of the MBH and its stellar environment. Galactic nuclei are astrophysical laboratories that test and challenge our understanding of MBH formation, strong gravity, stellar dynamics, and stellar physics. I review from a theoretical perspective the wide range of stellar phenomena that occur near MBHs, focusing on the role of stellar dynamics near an isolated MBH in a relaxed stellar cusp.
Thermally emitting X-ray isolated neutron stars represent excellent targets for testing cooling surface emission and atmosphere models, which are used to infer physical parameters of the neutron star. Among the seven known members of this class, RX J1605.3+3249 is the only one that still lacks confirmation of its spin period. Here we analyze NICER and XMM-Newton observations of RX J1605.3+3249, in order to address its timing and spectral behavior. Contrary to a previous tentative detection, but in agreement with the recent work by Pires et al. (2019), we find no significant pulsation with pulsed fraction higher than 1.3% (3{\sigma}) for periods above 150 ms. We also find a limit of 2.6% for periods above 2 ms, despite searches in different energy bands. The X-ray spectrum can be fit by either a double-blackbody model or by a single-temperature magnetized atmosphere model, both modified by a Gaussian absorption line at ~0.44 keV. The origin of the absorption feature as a proton cyclotron line or as an atomic transition in the neutron star atmosphere is discussed. The predictions of the best-fit X-ray models extended to IR, optical and UV bands are compared with archival data. Our results are interpreted in the framework of a fallback disk scenario.
We consider the comparison principle for semicontinuous viscosity sub- and supersolutions of second order elliptic equations on the form $F(D^2 w,x) = 0$. A structural condition on the operator is presented that seems to unify the different existing theories. A new result is obtained and the proofs of the classical results are simplified.
A collection of distinct sets is called a sunflower if the intersection of any pair of sets equals the common intersection of all the sets. Sunflowers are fundamental objects in extremal set theory with relations and applications to many other areas of mathematics as well as theoretical computer science. A central problem in the area due to Erd\H{o}s and Rado from 1960 asks for the minimum number of sets of size $r$ needed to guarantee the existence of a sunflower of a given size. Despite a lot of recent attention including a polymath project and some amazing breakthroughs, even the asymptotic answer remains unknown.   We study a related problem first posed by Duke and Erd\H{o}s in 1977 which requires that in addition the intersection size of the desired sunflower be fixed. This question is perhaps even more natural from a graph theoretic perspective since it asks for the Tur\'an number of a hypergraph made by the sunflower consisting of $k$ edges, each of size $r$ and with common intersection of size $t$. For a fixed size of the sunflower $k$, the order of magnitude of the answer has been determined by Frankl and F\"{u}redi. In the 1980's, with certain applications in mind, Chung, Erd\H{o}s and Graham and Chung and Erd\H{o}s considered what happens if one allows $k$, the size of the desired sunflower, to grow with the size of the ground set. In the three uniform case $r=3$ the correct dependence on the size of the sunflower has been determined by Duke and Erd\H{o}s and independently by Frankl and in the four uniform case by Buci\'{c}, Dragani\'{c}, Sudakov and Tran. We resolve this problem for any uniformity, by determining up to a constant factor the $n$-vertex Tur\'an number of a sunflower of arbitrary uniformity $r$, common intersection size $t$ and with the size of the sunflower $k$ allowed to grow with $n$.
Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized connections, ii) the difficulty of calculating its performance in practical regimes of both code size and logical error rate, and iii) the (perceived) need for large code sizes. Here we present numerical results indicating that the third assertion is false, and introduce a novel scheme that eliminates the two remaining problems while retaining a threshold very close to von Neumann's ideal of 1/6. We present a simple, highly ordered wiring structure that vastly reduces the circuit complexity, demonstrates that randomization is unnecessary, and provides a feasible method to calculate the performance. This in turn allows us to show that the scheme requires only moderate code sizes, vastly outperforms concatenation schemes, and under a standard error model a unitary implementation realizes universal FTCC with an accuracy threshold of p < 5.5%, in which p is the error probability for 3-qubit gates. FTCC is a key component in realizing measurement-free protocols for quantum information processing. In view of this we use our scheme to show that all-unitary quantum circuits can reproduce any measurement-based feedback process in which the asymptotic error probabilities for the measurement and feedback are 0.51p and 1.51p, respectively.
This work reports the detection of a multi peaked colour pattern in the integrated colours distribution of globular clusters associated to the giant elliptical galaxy NGC 4486, using Next Generation Virgo Survey data. This feature is imprinted on the well known bimodal colour distribution of these clusters. Remarkably, the pattern is similar to that found in previous works based on photometry from the HST Advanced Camera Virgo Survey, in less massive Virgo galaxies. This characteristic can be traced up to to 45 arcmin (217 Kpc) in galactocentric radius. This suggests that globular cluster formation in Virgo has been regulated, at least partially, by a collective process composed by several discrete events, working on spatial scales comparable to the size of the galaxy cluster. Furthermore, the presence of a similar colour pattern in NGC 5128, at the outskirsts of the Virgo Super-cluster, poses an intriguing question about the spatial scale of the phenomenon. The nature of the process that leads to the colour pattern is unknown. However, energetic events connected with galaxy or sub-galaxy cluster mergers and SMBH activity, in the early Universe, appear as possible candidates to explain an eventual enhancement/quenching of the globular clusters formation, reflected in the modulation of their integrated colours. Such events, presumably, may also have had an impact on the whole star formation history in Virgo galaxies.
Standard Model neutrinos are not usually considered plausible dark matter candidates because the usual treatment of their decoupling in the early universe implies that their mass must be sufficiently small to make them ``hot'' dark matter. In this paper we show that decoupling of Standard Model neutrinos in low reheat models may result in neutrino densities very much less than usually assumed, and thus their mass may be in the keV range. Standard Model neutrinos may therefore be warm dark matter candidates.
We model the detectability of exoplanets around stars in the Beta Pic Moving Group (BPMG) using the Gemini Planet Imager (GPI), a coronagraphic instrument designed to detect companions by imaging. Members of the BPMG are considered promising targets for exoplanet searches because of their youth (~12 MY) and proximity (median distance ~35 pc). We wrote a modeling procedure to generate hypothetical companions of given mass, age, eccentricity, and semi-major axis, and place them around BPMG members that fall within the V-band range of the GPI. We count as possible detections companions lying within the GPI's field of view and H-band fluxes that have a host-companion flux ratio placing them within its sensitivity. The fraction of companions that could be detected depends on their brightness at 12 Myr, and hence formation mechanism, and on their distribution of semi-major axes. We used brightness models for formation by disk instability and core-accretion. We considered the two extreme cases of the semi-major axis distribution - the log-normal distribution of the nearby F and G type stars and a power-law distribution indicated by the exoplanets detected by the radial velocity technique. We find that the GPI could detect exoplanets of all the F and G spectral type stars in the BPMG sample with a probability that depends on the brightness model and semi-major axis distribution. At spectral type K to M1, exoplanet detectability depends on brightness and hence distance of the host star. GPI will be able to detect the companions of M stars later than M1 only if they are closer than 10 pc. Of the four A stars in BPMG sample, only one has V-band brightness in the range of GPI; the others are too bright.
We present a determination of the distributions of gamma-ray photon flux -- the so called LogN-LogS relation -- and photon spectral index for blazars, based on the third extragalactic source catalog of the Fermi Gamma-ray Space Telescope's Large Area Telescope, and considering the photon energy range from 100 MeV to 100 GeV. The dataset consists of the 774 blazars in the so-called "Clean" sample detected with a greater than approximately seven sigma detection threshold and located above $\pm$20 deg Galactic latitude. We use non-parametric methods verified in previous works to reconstruct the intrinsic distributions from the observed ones which account for the data truncations introduced by observational bias and includes the effects of the possible correlation between the flux and photon index. The intrinsic flux distribution can be represented by a broken power law with a high flux power-law index of -2.43$\pm$0.08 and a low flux power-law index of -1.87$\pm$0.10. The intrinsic photon index distribution can be represented by a Gaussian with mean of 2.62$\pm$0.05 and width of 0.17$\pm$0.02. We also report the intrinsic distributions for the sub-populations of BL Lac and FSRQ type blazars separately and these differ substantially. We then estimate the contribution of FSRQs and BL Lacs to the diffuse extragalactic gamma-ray background radiation. Under the simplistic assumption that the flux distributions probed in this analysis continue to arbitrary low flux, we calculate that the best fit contribution of FSRQs is 35% and BL Lacs 17% of the total gamma-ray output of the Universe in this energy range.
Emission process of a charged particle propagating in a medium with a curved magnetic field is considered. This mechanism combines features of conventional Cherenkov and curvature emission. Thus, presence of a medium with the index of refraction larger than the unity is essential for the emission. In the present paper the generation of high frequency radiation by the mentioned mechanism is considered. The generated waves are vacuum-like electromagnetic waves and may leave the medium directly. Consequently, this emission mechanism may be important for the problem of pulsar X-ray and gamma-ray emission generation.
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
We describe a model for pion production off nucleons and coherent pions from nuclei induced by neutrinos in the 1 GeV energy regime. Besides the dominant Delta pole contribution, it takes into account the effect of background terms required by chiral symmetry. Moreover, the model uses a reduced nucleon-to-Delta resonance axial coupling, which leads to coherent pion production cross sections around a factor two smaller than most of the previous theoretical estimates. Nuclear effects like medium corrections on the Delta propagator and final pion distortion are included.
We develop a first-principles theory of phonon-assisted optical absorption in semiconductors and insulators which incorporates the temperature dependence of the electronic structure. We show that the Hall-Bardeen-Blatt theory of indirect optical absorption and the Allen-Heine theory of temperature-dependent band structures can be derived from the present formalism by retaining only one-phonon processes. We demonstrate this method by calculating the optical absorption coefficient of silicon using an importance sampling Monte Carlo scheme, and we obtain temperature-dependent lineshapes and band gaps in good agreement with experiment. The present approach opens the way to predictive calculations of the optical properties of solids at finite temperature.
In this article we initiate the study of 1+ 2 dimensional wave maps on a curved spacetime in the low regularity setting. Our main result asserts that in this context the wave maps equation is locally well-posed at almost critical regularity.   As a key part of the proof of this result, we generalize the classical optimal bilinear L^2 estimates for the wave equation to variable coefficients, by means of wave packet decompositions and characteristic energy estimates. This allows us to iterate in a curved X^{s,b} space.
Galaxy clusters at high redshift are key targets for understanding matter assembly in the early Universe, yet they are challenging to locate. A sample of >2000 high-z candidate structures has been found using Planck's all-sky submm maps, and a sub-set of 234 have been followed up with Herschel-SPIRE, which showed that the emission can be attributed to large overdensities of dusty star-forming galaxies. In order to resolve and characterise the individual galaxies we targeted the eight brightest SPIRE sources in the centre of the Planck peak PLCK G073.4-57.5 using ALMA at 1.3 mm, and complemented these observations with data from IRAC, WIRCam J,K, and SCUBA-2. We detected a total of 18 millimetre galaxies brighter than 0.3 mJy in 2.4 arcmin^2. The ALMA source density is 8-30 times higher than average background estimates and larger than seen in typical 'proto-cluster' fields. We were able to match all but one of the ALMA sources to a NIR counterpart. The most significant (four) SCUBA-2 sources are not included in the ALMA pointings, but we find an 8sigma stacking detection of the ALMA sources in the SCUBA-2 map at 850 um. We derive photo-z, L_IR, SFR, stellar mass, T_dust, M_dust for all of the ALMA galaxies; the photo-zs identify two groups each of five sources, at z~1.5 and 2.4. The two groups show two 'red sequences' (i.e. similar NIR [3.6]-[4.5] colours and different J-K colours). The majority of the ALMA-detected galaxies are on the SFR versus stellar mass main sequence, and half of the sample is more massive than the characteristic stellar mass at the corresponding redshift. Serendipitous CO line detections in two of the galaxies appear to match their photometric redshifts at z~1.54. We performed an analysis of star-formation efficiencies and CO- and mm-continuum-derived gas fractions of our ALMA sources, combined with a sample of 1<z<3 cluster and proto-cluster members.
A long debated issue concerning the nucleosynthesis of neutron-rich elements in Asymptotic Giant Branch (AGB) stars is the identification of the neutron source. We report intermediate-mass (4 to 8 solar masses) AGB stars in our Galaxy that are rubidium-rich owing to overproduction of the long-lived radioactive isotope 87Rb, as predicted theoretically 40 years ago. This represents a direct observational evidence that the 22Ne(alpha,n)25Mg reaction must be the dominant neutron source in these stars. These stars then challenge our understanding of the late stages of the evolution of intermediate-mass stars and would promote a highly variable Rb/Sr environment in the early solar nebula.