ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose an extension of the Ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group. This model is primarily motivated by a natural approximation to the so-called spatial random permutations recently studied by V. Betz and D. Ueltschi (hence the name "surrogate-spatial"), but it is of substantial interest in its own right. We show that under the suitable (thermodynamic) limit both measures have the similar critical behaviour of the cycle statistics characterized by the emergence of infinitely long cycles. Moreover, using a greater analytic tractability of the surrogate-spatial model, we obtain a number of new results about the asymptotic distribution of the cycle lengths (both small and large) in the full range of subcritical, critical and supercritical domains. In particular, in the supercritical regime there is a parametric "phase transition" from the Poisson-Dirichlet limiting distribution of ordered cycles to the occurrence of a single giant cycle. Our techniques are based on the asymptotic analysis of the corresponding generating functions using Polya's Enumeration Theorem and complex variable methods.
H. W. Lenstra \cite{lenstra} introduced the notion of an Euclidean ideal class, which is a generalization of norm-Euclidean ideals in number fields. Later, families of number fields of small degree were obtained with an Euclidean ideal class (for instance, in \cite{hester1} and \cite{cathy}). In this paper, we construct certain new families of biquadratic number fields having a non-principal Euclidean ideal class and this extends the previously known families given by H. Graves \cite{hester1} and C. Hsu \cite{cathy}.
We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites of hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behavour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.
Until recently, only science-fiction authors ventured to use a term teleportation. However, in the last few years, on the eve of upcoming new millennium, the situation changed very much. The present report gives a synopsis of main concepts in this area. The readers will be able to make sure that paradoxical phenomena in the microcosm give a possibility to demonstrate the exchange of properties between microobjects, removed at a very large distance from each other, when no forces act between them. A new experimental scheme with hydrogen and helium nuclei is proposed. It is expected that the results of these experiments will be considered as teleportation of nuclear properties of atoms of the simplest chemical elements. A problem of teleportation of the more palpable cargo is left to the physics of the more distant future.
One of the main problems in Particle Physics is to understand the origin and nature of Dark Matter. An exciting possibility is to consider that the Dark Matter belongs to a new complex but hidden sector. In this paper, we assume the existence of a strongly interacting dark sector consisting on a new scalar doublet and new vector resonances, in concordance with a model recently proposed by our group. Since in a previous work it was found that it is very challenging to find the new vector resonances at the LHC, here we study the possibility of finding them at the a future Compact Linear Collider (CLIC) running at $\sqrt{s}=3$ TeV. We consider two distinct scenarios: when the non-standard scalars are heavy, the dark resonance is intense enough to make its discovery possible at CLIC when the resonance mass is in the range $[2000,3000]$ GeV. In the second scenario, when the non-standard scalars are light, the new vector boson is too broad to be recognized as a resonance and is not detectable except when the mass of the scalars is close to (but smaller than) a half of the resonance mass and the scale of the dark sector is high. In all the positive cases, less than a tenth of the maximum integrated luminosity is needed to reach the discovery level. Finally, we also comment about the mono-$Z$ production.
We describe a new mechanism leading to the formation of rational magnetization plateau phases, which is mainly due to the anharmonic spin-phonon coupling. This anharmonicity produces plateaux in the magnetization curve at unexpected values of the magnetization without explicit magnetic frustration in the Hamiltonian and without an explicit breaking of the translational symmetry. These plateau phases are accompanied by magneto-elastic deformations which are not present in the harmonic case.
We present a simple, physically-motivated model to interpret consistently the emission from galaxies at ultraviolet, optical and infrared wavelengths. We combine this model with a Bayesian method to obtain robust statistical constraints on key parameters describing the stellar content, star formation activity and dust content of galaxies. Our model is now publicly available via a user-friendly code package, MAGPHYS at www.iap.fr/magphys. We present an application of this model to interpret a sample of ~1400 local (z<0.5) galaxies from the H-ATLAS survey. We find that, for these galaxies, the diffuse interstellar medium, powered mainly by stars older than 10 Myr, accounts for about half the total infrared luminosity. We discuss the implications of this result to the use of star formation rate indicators based on total infrared luminosity.
We present a novel online unsupervised method for face identity learning from video streams. The method exploits deep face descriptors together with a memory based learning mechanism that takes advantage of the temporal coherence of visual data. Specifically, we introduce a discriminative feature matching solution based on Reverse Nearest Neighbour and a feature forgetting strategy that detect redundant features and discard them appropriately while time progresses. It is shown that the proposed learning procedure is asymptotically stable and can be effectively used in relevant applications like multiple face identification and tracking from unconstrained video streams. Experimental results show that the proposed method achieves comparable results in the task of multiple face tracking and better performance in face identification with offline approaches exploiting future information. Code will be publicly available.
Deep image generation is becoming a tool to enhance artists and designers creativity potential. In this paper, we aim at making the generation process more structured and easier to interact with. Inspired by vector graphics systems, we propose a new deep image reconstruction paradigm where the outputs are composed from simple layers, defined by their color and a vector transparency mask. This presents a number of advantages compared to the commonly used convolutional network architectures. In particular, our layered decomposition allows simple user interaction, for example to update a given mask, or change the color of a selected layer. From a compact code, our architecture also generates vector images with a virtually infinite resolution, the color at each point in an image being a parametric function of its coordinates. We validate the efficiency of our approach by comparing reconstructions with state-of-the-art baselines given similar memory resources on CelebA and ImageNet datasets. Most importantly, we demonstrate several applications of our new image representation obtained in an unsupervised manner, including editing, vectorization and image search.
We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.
A simple proof of quantum adiabatic theorem is provided. Quantum adiabatic approximation is divided into two kinds. For Hamiltonian H(t/T), a relation between the size of the error caused by quantum adiabatic approximation and the parameter T is given.
In his previous paper, the author proposed as a problem a purely inseparable analogue of the Abhyankar conjecture for affine curves in positive characteristic and gave a partial answer to it, which includes a complete answer for finite local nilpotent group schemes. In the present paper, motivated by the Abhyankar conjectures with restricted ramifications due to Harbater and Pop, we study a refined version of the analogous problem, based on a recent work on tamely ramified torsors due to Biswas-Borne, which is formulated in terms of root stacks. We study an embedding problem to conclude that the refined analogue is true in the solvable case.
The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that \emph{quantum particles} of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state--in clear conflict with what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles \emph{emerge}, as new entities that do not correspond to the "particle indices" defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to \emph{particles}, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether the discussions about the status of identical quantum particles have not been misguided from the very start.
We study in special limiting cases quasinormal modes of massive scalar fields in the Schwarzschild-de Sitter black hole backgrounds. We determine the lower limit on the mass parameter of the scalar field that allows the waves with quasinormal frequencies to propagate to infinity, showing that it depends on the spacetime parameters only. Then we discuss in the large multipole number limit quasinormal modes, whose frequencies can be directly related to the unstable circular photon geodesics. In the large scalar mass approximation, we demonstrate the new interesting phenomenon of slowly decaying resonances, that are strongly related to the maximum of the effective potential of the massive scalar field, which is located at the static radius of the Schwarzschild-de Sitter spacetimes, where the cosmic repulsion is just balanced by the black hole attraction.
The rapidly expanding research in Spintronics, the electronics utilizing the electron spin instead of its charge, is driven by the very interesting potential applications. The actual task is to develop principles for the spin manipulations in spintronic devices. In this Report we suggest and verify experimentally a concept of heteromagnetic semiconductor structures. It is based on spin diffusion between layers of the nanostructure with different magnetic properties and allows controlling the spin-switching rate for magnetic ions. A ten times increase of spin-lattice relaxation rate of magnetic Mn-ions is achieved in (Zn,Mn)Se/(Be,Mn)Te heteromagnetic structures with an inhomogeneous distribution of Mn-ions.
The statistics of peaks of the initial, Gaussian density field can be used to interpret the abundance and clustering of massive dark matter haloes. I discuss some recent theoretical results related to their clustering and its redshift evolution. Predictions from the peak model are qualitatively consistent with measurements of the linear bias of high mass haloes, which also show some evidence for a dependence on the halo mass M at fixed peak height. The peak approach also predicts a distinctive scale-dependence in the bias of haloes across the baryon acoustic feature, a measurement of which would provide strong support for its validity. For 2-sigma density peaks collapsing at z=0.3, this residual scale-dependent bias is at the 5-10 percent level and should thus be within reach of very large simulations of structure formation.
This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low energy spin excitations consist of a few different spin multiplets $|S_{i}M_{i}>$. Under certain conditions (to be explained below) some of the lowest energy levels $E_{S_{i}}$ are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top in the sense that beside its spin operator other dot (vector) operators ${\bf R}_{n}$ are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets $<S_{i}M_{i} |{\bf R}_{n}|S_{j}M_{j} > \ne 0$. These "Runge-Lenz" operators do not appear in the isolated dot-Hamiltonian (so in some sense they are "hidden"). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin ${\bf s}$ with the operators of the dot then contains new exchange terms, $J_{n} {\bf s} \cdot {\bf R}_{n}$ beside the ubiquitous ones $J_{i} {\bf s}\cdot {\bf S}_{i}$. The operators ${\bf S}_{i}$ and ${\bf R}_{n}$ generate a dynamical group (usually SO(n)). Remarkably, the value of $n$ can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied then, under favorable circumstances, the exchange interaction involves solely the Runge-Lenz operators ${\bf R}_{n}$ and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in triple quantum dot with four electrons.
We developed a solar flare prediction model using a deep neural network (DNN), named Deep Flare Net (DeFN). The model can calculate the probability of flares occurring in the following 24 h in each active region, which is used to determine the most likely maximum classes of flares via a binary classification (e.g., >=M class versus <M class or >=C class versus <C class). From 3x10^5 observation images taken during 2010-2015 by Solar Dynamic Observatory, we automatically detected sunspots and calculated 79 features for each region, to which flare occurrence labels of X-, M-, and C-class were attached. We adopted the features used in Nishizuka et al. (2017) and added some features for operational prediction: coronal hot brightening at 131 A (T>=10^7 K) and the X-ray and 131 A intensity data 1 and 2 h before an image. For operational evaluation, we divided the database into two for training and testing: the dataset in 2010-2014 for training and the one in 2015 for testing. The DeFN model consists of deep multilayer neural networks, formed by adapting skip connections and batch normalizations. To statistically predict flares, the DeFN model was trained to optimize the skill score, i.e., the true skill statistic (TSS). As a result, we succeeded in predicting flares with TSS=0.80 for >=M-class flares and TSS=0.63 for >=C-class flares. Note that in usual DNN models, the prediction process is a black box. However, in the DeFN model, the features are manually selected, and it is possible to analyze which features are effective for prediction after evaluation.
The quantum $XY$ spin chain with the interactions decaying as a power law $1/r^{1+ \sigma}$ of the distance between spins $r$ was investigated with the exact diagonalization method. Here, the constituent spin is set to $S=1$, which enables us to incorporate the biquadratic interactions so as to realize the order-disorder transition with the O$(2)$ symmetry maintained. Thereby, in the ordered phase, we resolved the Higgs mass $m_H$ out of the Goldstone-excitation continuum by specifying Higgs-particle's quantum numbers to adequate indices. We then turn to the analysis of the critical amplitude ratio $m_H / \Delta$ ($\Delta$: paramagnetic gap in the disordered phase). As the power of the algebraic decay $\sigma$ increases, the amplitude ratio $m_H/\Delta$ gets enhanced gradually in agreement with the $\epsilon(=4-D)$-expansion-renormalization-group result; here, we resort to the $\sigma \leftrightarrow D$ relation advocated recently in order to establish a relationship between the renormalization-group result and ours.
The present paper intends to be a new study of a widely used precursor in nanostructure deposition and FEBID processes with a focus on its fragmentation at collisions with low-energy electrons. Newer developments in nanotechnology with applications to Focused Electron Beam Induced Deposition (FEBID) and Extreme Ultraviolet Lithography (EUVL), based on irradiation-induced chemistry come with advances in the size of the nanostructures at the surface and their flexibility in creating highly complex 3D structures. The deformation in the main structures of the FEBID process characterized by elongation, reduction in diameter of the main structure, and the deposition of additional thin layers around the structure on the substrate are results of the effect of the secondary electrons, olliding with energies lower than 20eV. Fe(CO)5 is one of the most used compounds in FEBID processes as it has high pressure and has been shown to provide high purity deposits (over 90%). This paper combines experiment and simulations to study electron scattering from Fe(CO)5, while experimental data on dissociative electron attachment is presented using the Velocity Slice Map Imaging (VMI) technique that combined with data collected on the CLUSTER apparatus at Comenius University, Bratislava and Quantemol-N simulations present the fragmentation pathways and channel distribution for each of the resulting negative ions at low energies. The Quantemol-N simulation package is used to study collision processes of low-energy electrons with Fe(CO)5 molecules including elastic, electronic excitation, and dissociative electron attachment (DEA) cross-sections.
Recent works have proven that many relevant visual tasks are closely related one to another. Yet, this connection is seldom deployed in practice due to the lack of practical methodologies to transfer learned concepts across different training processes. In this work, we introduce a novel adaptation framework that can operate across both task and domains. Our framework learns to transfer knowledge across tasks in a fully supervised domain (e.g., synthetic data) and use this knowledge on a different domain where we have only partial supervision (e.g., real data). Our proposal is complementary to existing domain adaptation techniques and extends them to cross tasks scenarios providing additional performance gains. We prove the effectiveness of our framework across two challenging tasks (i.e., monocular depth estimation and semantic segmentation) and four different domains (Synthia, Carla, Kitti, and Cityscapes).
Given an arbitrary state $\rho$ and some figure of merit ${\cal E}(\rho)$, it is usually a hard problem to determine the value of ${\cal E}(\rho^{\otimes N})$. One noticeable exception is the case of additive measures, for which we simply have ${\cal E}(\rho^{\otimes N}) = Ne$, with $e\equiv {\cal E}(\rho)$. In this work we study measures that can be described by ${\cal E}(\rho^{\otimes N}) =E(e;N) \ne Ne$, that is, measures for which the amount of resources of $N$ copies is still determined by the single real variable $e$, but in a nonlinear way. If, in addition, the measures are analytic around $e=0$, recurrence relations can be found for the Maclaurin coefficients of $E$ for larger $N$. As an example, we show that the $\ell_1$-norm of coherence is a nontrivial case of such a behavior.
Gravitational coupling of the propagation four-vectors of matter wave functions is formulated in flat space-time. Coupling at the momentum level rather than at the "force-law" level greatly simplifies many calculations. This locally Lorentz-invariant approach (G4v) treats electromagnetic and gravitational coupling on an equal footing. Classical mechanics emerges from the incoherent aggregation of matter wave functions. The theory reproduces, to first order beyond Newton, the standard GR results for Gravity-Probe B, deflection of light by massive bodies, precession of orbits, gravitational red shift, and total gravitational-wave energy radiated by a circular binary system. Its predictions of total radiated energy from highly eccentric Kepler systems are slightly larger than those of similar GR treatments. G4v predictions differ markedly from those of GR for the gravitational-wave radiation patterns from rotating massive systems, and for the LIGO antenna pattern. The predicted antenna patterns have been shown to be highly distinguishable in the case of continuous gravitational-wave sources, and should therefore be testable as data from Advanced LIGO becomes available over the next few years.
Investigating in detail the physics of energy filtering through a single planar energy barrier in nanostructured thermoelectric generators, we reinforce the non-trivial result that the anticipated enhancement in generated power at a given efficiency via energy filtering is a characteristic of systems dominated by incoherent scattering and is absent in ballistic devices. In such cases, assuming an energy dependent relaxation time $\tau(E)=kE^r$, we show that there exists a minimum value $r_{min}$ beyond which generation can be enhanced by embedding nanobarriers. For bulk generators with embedded nanobarriers, we delve into the details of inter sub-band scattering and show that it has finite contribution to the enhancement in generation. We subsequently discuss the realistic aspects, such as the effect of smooth transmission cut-off and show that for $r>r_{min}$, the optimized energy barrier is just sufficiently wide enough to scatter off low energy electrons, a very wide barrier being detrimental to the performance. Analysis of the obtained results should provide general design guidelines for enhancement in thermoelectric generation via energy filtering. Our non-equilibrium approach is typically valid in the absence of local quasi-equilibrium and hence sets the stage for future advancements in thermoelectric device analysis, for example, Peltier cooling near a barrier interface.