ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost particle gets a constant drift to the right, we derive and solve the corresponding one- sided Stefan (free-boundary) equations. Via this solution we explicitly determine the limiting particle-density profile as well as the asymptotic trajectory of the leftmost particle. While doing so we further establish stochastic domination and convergence to equilibrium results for the vector of relative spacings among the leading particles.
In this paper, we study the long-term asymptotics for the quenched moment \[\mathbb{E}_x\exp \biggl\{\int_0^tV(B_s)\,ds\biggr\}\] consisting of a $d$-dimensional Brownian motion $\{B_s;s\ge 0\}$ and a generalized Gaussian field $V$. The major progress made in this paper includes: Solution to an open problem posted by Carmona and Molchanov [Probab. Theory Related Fields 102 (1995) 433-453], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional white noise.
With their sizes larger than 0.7 Mpc, Giant Radio Galaxies (GRGs) are the largest individual objects in the Universe. To date, the reason why they reach such enormous extensions is still unclear. One of the proposed scenarios suggests that they are the result of multiple episodes of jet activity. Cross-correlating the INTEGRAL+Swift AGN population with radio catalogues (NVSS, FIRST, SUMSS), we found that 22% of the sources are GRG (a factor four higher than those selected from radio catalogues). Remarkably, 80% of the sample shows signs of restarting radio activity. The X-ray properties are consistent with this scenario, the sources being in a high-accretion, high-luminosity state with respect to the previous activity responsible for the radio lobes.
We analyse the effect of synchronization between noise and periodic signal in a two-state spatially extended system analytically. Resonance features are demonstrated. To have the maximum cooperation between signal and noise, it is shown that noise strength at resonance should increase linearly with the frequency of the signal. The time scale of the process at resonance is also shown to increase linearly with the period of the signal.
We introduce a formalism that connections entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in quant-ph/0104095 by Eggeling et al., namely that on copy of any bipartite state with non--positive partial transpose (NPPT) is either distillable, or activable. Second, we show that there exist three--partite NPPT states, with the property that two copies can neither be distilled, nor activated.
The moduli spaces of flat $\mathrm{SL}_2$- and $\mathrm{PGL}_2$-connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tam\'as Hausel in Remark 3.30 of "Global topology of the Hitchin system".
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of the first-passage times, i.e. the time delays after which the counting variable reaches a certain threshold value, is studied. This paper presents the approach to calculate the first-passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the Markovian network. Using this approach it is shown that when the subsequent first-passage times are uncorrelated there exist strict relations between the cumulants of the full counting statistics and the first-passage time distribution. On the other hand, when the correlations of the first-passage times are present, their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics; for example, it may reveal the switching between different dynamical states of the system. Additionally, I show that breaking of the fluctuation theorem for first-passage times may reveal the multicyclic nature of the Markovian network.
In this paper we are concerned with the SIR model with random vertex weights on Erd\H{o}s-R\'{e}nyi graph $G(n,p)$. The Erd\H{o}s-R\'{e}nyi graph $G(n,p)$ is generated from the complete graph $C_n$ with $n$ vertices through independently deleting each edge with probability $(1-p)$. We assign i. i. d. copies of a positive r. v. $\rho$ on each vertex as the vertex weights. For the SIR model, each vertex is in one of the three states `susceptible', `infective' and `removed'. An infective vertex infects a given susceptible neighbor at rate proportional to the production of the weights of these two vertices. An infective vertex becomes removed at a constant rate. A removed vertex will never be infected again. We assume that at $t=0$ there is no removed vertex and the number of infective vertices follows a Bernoulli distribution $B(n,\theta)$. Our main result is a law of large numbers of the model. We give two deterministic functions $H_S(\psi_t), H_V(\psi_t)$ for $t\geq 0$ and show that for any $t\geq 0$, $H_S(\psi_t)$ is the limit proportion of susceptible vertices and $H_V(\psi_t)$ is the limit of the mean capability of an infective vertex to infect a given susceptible neighbor at moment $t$ as $n$ grows to infinity.
In this paper we introduce the notion of Blow-semialgebraic triviality consistent with a compatible filtration for an algebraic family of algebraic sets, as an equisingularity for real algebraic singularities. Given an algebraic family of 3-dimensional algebraic sets defined over a nonsingular algebraic variety, we show that there is a finite subdivision of the parameter algebraic set into connected Nash manifolds over which the family admits a Blow-semialgebraic trivialisation consistent with a compatible filtration. We show a similar result on finiteness also for a Nash family of 3-dimensional Nash sets through the Artin-Mazur theorem. As a corollary of the arguments in their proofs, we have a finiteness theorem on semialgebraic types of polynomial mappings from the 2-dimensional Euclidean space to the p-diemnsional Euclidean space.
A commensurate-incommensurate phase transition in bilayer graphene is investigated in the framework of the Frenkel-Kontorova model extended to the case of two interacting chains of particles. Analytic expressions are derived to estimate the critical unit elongation of one of the graphene layers at which the transition to the incommensurate phase takes place, the length and formation energy of incommensurability defects (IDs) and the threshold force required to start relative motion of the layers on the basis of dispersion-corrected density functional theory calculations of the interlayer interaction energy as a function of the relative position of the layers. These estimates are confirmed by atomistic calculations using the DFT-D based classical potential. The possibility to measure the barriers for relative motion of graphene layers by the study of formation of IDs in bilayer graphene is discussed.
We performed 12CO(1-0), 13CO(1-0), and HCN(1-0) single-dish observations (beam size ~14"-18") toward nearby starburst and non-starburst galaxies using the Nobeyama 45 m telescope. The 13CO(1-0) and HCN(1-0) emissions were detected from all the seven starburst galaxies, with the intensities of both lines being similar (i.e., the ratios are around unity). On the other hand, for case of the non-starburst galaxies, the 13CO(1-0) emission was detected from all three galaxies, while the HCN(1-0) emission was weakly or not detected in past observations. This result indicates that the HCN/13CO intensity ratios are significantly larger (~1.15+-0.32) in the starburst galaxy samples than the non-starburst galaxy samples (<0.31+-0.14). The large-velocity-gradient model suggests that the molecular gas in the starburst galaxies have warmer and denser conditions than that in the non-starburst galaxies, and the photon-dominated-region model suggests that the denser molecular gas is irradiated by stronger interstellar radiation field in the starburst galaxies than that in the non-starburst galaxies. In addition, HCN/13CO in our sample galaxies exhibit strong correlations with the IRAS 25 micron flux ratios. It is a well established fact that there exists a strong correlation between dense molecular gas and star formation activities, but our results suggest that molecular gas temperature is also an important parameter.
Since the discovery of the spin orbit torque (SOT) induced by spin Hall effect in heavy metals, much effort has been devoted to understanding the mechanism of the charge-to-spin conversion as well as to developing new schemes for high speed, low energy magnetic recording technologies. While fast switching has been demonstrated in three terminal magnetic tunnel junctions (3T-MTJs) through applying short voltage pulses in the heavy metal channel, detailed understanding of the switching mechanism is lacking due to the complexity of the multi-layered magnetic structure and the three-terminal geometry. We show in this letter that current-induced effective fields play a key role in the fast switching and by tuning the applied external field we can finely tune the symmetry of the pulse switching between two switching polarities, namely parallel to anti-parallel (P-AP) and anti-parallel to parallel (AP-P). These results show that the manipulation of detailed magnetic configuration is the key to fast switching and is a useful way for future optimization of SOT memory and further applications.
In this article, we generalize the work of H.Hida and V.Pilloni to construct $p$-adic families of $\mu$-ordinary modular forms on Shimura varieties of Hodge type $Sh(G,X)$ associated to a Shimura datum $(G,X)$ where $G$ is a connected reductive group over $\mathbb{Q}$ and is unramified at $p$, such that the adjoint quotient $G^\mathrm{ad}$ has no simple factors isomorphic to $\mathrm{PGL}_2$.
While active galactic nuclei with relativistic jets have long been prime candidates for the origin of extragalactic cosmic rays and neutrinos, the BL Lac object TXS 0506+056 is the first astrophysical source observed to be associated with some confidence ($\sim 3\sigma$) with a high-energy neutrino, IceCube-170922A, detected by the IceCube Observatory. The source was found to be active in high-energy gamma-rays with Fermi-LAT and in very-high-energy gamma-rays with the MAGIC telescopes. To consistently explain the observed neutrino and multi-wavelength electromagnetic emission of TXS 0506+056, we investigate in detail single-zone models of lepto-hadronic emission, assuming co-spatial acceleration of electrons and protons in the jet, and synchrotron photons from the electrons as targets for photo-hadronic neutrino production. The parameter space concerning the physical conditions of the emission region and particle populations is extensively explored for scenarios where the gamma-rays are dominated by either 1) proton synchrotron emission or 2) synchrotron-self-Compton emission, with a subdominant but non-negligible contribution from photo-hadronic cascades in both cases. We find that the latter can be compatible with the neutrino observations, while the former is strongly disfavoured due to the insufficient neutrino production rate.
In this paper we establish the existence of mountain pass and negative energy weak solutions for a Kirchhoff-Schr\"odinger type problem in $\mathbb R^4$ involving a critical nonlinearity and a suitable small perturbation. The arisen competition between the terms due to the nonlocal coefficient and critical nonlinearity turns out to be rather interesting. The main tools used in the present work are variational methods and the Lions' Concentration Compactness Principle.
Molecular dynamics (MD) simulations of complex electrochemical systems, such as ionic liquid supercapacitors, are increasingly including the constant potential method (CPM) to model conductive electrodes at specified potential difference, but the inclusion of CPM can be computationally expensive. We demonstrate the computational savings available in CPM MD simulations of ionic liquid supercapacitors when the usual non-periodic slab geometry is replaced with fully periodic boundary conditions. We show how a doubled cell approach, previously used in non-CPM MD simulations of charged interfaces, can be used to enable fully periodic CPM MD simulations. Using either a doubled cell approach, or a finite field approach previously reported by others, fully periodic CPM MD simulations produce comparable results to the traditional slab geometry simulations with a nearly double speed-up in computational time. Indeed, these savings can offset the additional cost of the CPM algorithm, resulting in periodic CPM MD simulations that are faster than the non-periodic, fixed-charge equivalent simulations for the ionic liquid supercapacitors studied here.
In this paper, we construct an infinite family of elliptic curves whose rank is exactly two and the torsion subgroup is a cyclic group of order two or three, under the parity conjecture.
We propose the origins of Dark Energy in a hidden sector with a pair of very light fermions, oppositely charged under an abelian gauge force $U(1)_X$ but of unequal mass. The system is dubbed PAAI, plasma which is abelian, asymmetric and idealised. For a range of the hidden fine structure constant values and the value of mass of the lightest fermion the PAAI is argued to simulate Dark Energy. Additional fermions from the same sector are shown to account for Dark Matter. Further, residual $X$-magnetic fields can mix with Maxwell electromagnetism to provides the seed for cosmic-scale magnetic fields. Thus the scenario can explain several cosmological puzzles from within the same hidden sector.
Here we present a reconstruction of the Positive Operator-Value Measurement of a photon-number-resolving detector comprised of three 50:50 beamsplitters in a tree configuration, terminated with four single-photon avalanche detectors. The four detectors' outputs are processed by an electronic board that discriminates detected photon number states from 0 to 4 and implements a "smart counting" routine to compensate for dead time issues at high count rates.
Although measuring the gas metallicity in galaxies at various redshifts is crucial to constrain galaxy evolutionary scenarios, only rest-frame optical emission lines have been generally used to measure the metallicity. This has prevented us to accurately measure the metallicity of dust-obscured galaxies, and accordingly to understand the chemical evolution of dusty populations, such as ultraluminous infrared galaxies. Here we propose diagnostics of the gas metallicity based on infrared fine structure emission lines, which are nearly unaffected by dust extinction even the most obscured systems. Specifically, we focus on fine-structure lines arising mostly from HII regions, not in photo-dissociation regions, to minimize the dependence and uncertainties of the metallicity diagnostics from various physical parameters. Based on photoionization models, we show that the emission-line flux ratio of ([OIII]51.80+[OIII]88.33)/[NIII]57.21 is an excellent tracer of the gas metallicity. The individual line ratios [OIII]51.80/[NIII]57.21 or [OIII]88.33/[NIII]57.21 can also be used as diagnostics of the metallicity, but they suffer a stronger dependence on the gas density. The line ratios [OIII]88.33/[OIII]51.80 and [NII]121.7/[NIII]57.21 can be used to measure and, therefore, account for the dependences on the of the gas density and ionization parameter, respectively. We show that these diagnostic fine-structure lines are detectable with Herschel in luminous infrared galaxies out z=0.4. Metallicity measurements with these fine-structure lines will be feasible at relatively high redshift (z=1 or more) with SPICA, the future infrared space observatory.
A particular population of galaxies have drawn much interest recently, which are as faint as typical dwarf galaxies but have the sizes as large as $L^*$ galaxies, the so called "ultra-diffuse galaxie" (UDGs). The lack of tidal features of UDGs in dense environments suggests that their host halos are perhaps as massive as that of the Milky Way. On the other hand, galaxy formation efficiency should be much higher in the halos of such masses. Here we use the model galaxy catalog generated by populating two large simulations: the Millennium-II cosmological simulation and Phoenix simulations of 9 big clusters with the semi-analytic galaxy formation model. This model reproduces remarkably well the observed properties of UDGs in the nearby clusters, including the abundance, profile, color, and morphology, etc. We search for UDG candidates using the public data and find 2 UDG candidates in our Local Group and 23 in our Local Volume, in excellent agreement with the model predictions. We demonstrate that UDGs are genuine dwarf galaxies, formed in the halos of $\sim 10^{10}M_{\odot}$. It is the combination of the late formation time and high-spins of the host halos that results in the spatially extended feature of this particular population. The lack of tidal disruption features of UDGs in clusters can also be explained by their late infall-time.
We compute the entropy of systems of quantum particles satisfying the fractional exclusion statistics in the space-time of 2+1 dimensional black hole by using the brick-wall method. We show that the entropy of each effective quantum field theory with a Planck scale ultraviolet cutoff obeys the area law, irrespective of the angular momentum of the black hole and the statistics interpolating between Bose-Einstein and Fermi-Dirac statistics.
Deep neural networks (DNNs) are so over-parametrized that recent research has found them to already contain a subnetwork with high accuracy at their randomly initialized state. Finding these subnetworks is a viable alternative training method to weight learning. In parallel, another line of work has hypothesized that deep residual networks (ResNets) are trying to approximate the behaviour of shallow recurrent neural networks (RNNs) and has proposed a way for compressing them into recurrent models. This paper proposes blending these lines of research into a highly compressed yet accurate model: Hidden-Fold Networks (HFNs). By first folding ResNet into a recurrent structure and then searching for an accurate subnetwork hidden within the randomly initialized model, a high-performing yet tiny HFN is obtained without ever updating the weights. As a result, HFN achieves equivalent performance to ResNet50 on CIFAR100 while occupying 38.5x less memory, and similar performance to ResNet34 on ImageNet with a memory size 26.8x smaller. The HFN will become even more attractive by minimizing data transfers while staying accurate when it runs on highly-quantized and randomly-weighted DNN inference accelerators. Code available at https://github.com/Lopez-Angel/hidden-fold-networks
Osmotic energy (or salinity-gradient energy) is the energy released when water with different salinities is mixed, such as rivers and oceans. By employing a semipermeable membrane to control the mixing process, the osmotic pressure gradient energy can be generated in terms of electrical power via pressure retarded osmosis (PRO) without causing adverse environmental impacts. This work presents the fabrication of thin film nanocomposite (TFN) membranes which are customized to offer high flux in forward osmosis (FO) and high osmotic power in PRO. In this study, the TFN membrane was fabricated by forming a polyamide thin film on the polysulfone substrate through the interfacial polymerization process. One of the challenges in this process is the fouling of PRO membranes. Fouling is one of the major characteristics that results in the decline in the water flux of the membrane. The hydraulic pressure during PRO processes is less than RO processes so membranes that are used for PRO are less likely to foul. Experiments show that TFN membranes are more tolerant of fouling than TFC membranes because of the nanomaterials which has higher surface hydrophilicity. The structure of the membrane is a very significant characteristic that has an influence on fouling. Especially, the structure of porosity that is coherent to the thickness.
Studying nonsupersymmetric yet imaginary self-dual three-form fluxes in type IIB supergravity backgrounds on Sasaki-Einstein manifolds we find a new analytic solution that restores supersymmetry in the IR, breaks it at higher energies, yet suffers from curvature singularities in the UV, when a certain SUSY-breaking parameter becomes large. Consequently we investigate a variety of possibilities to cure the singularity by either introducing additional sources, changing the fluxes or deforming the geometry. Since it is not possible to cure the singularities making physically reasonably assumptions, we suggest that there might be a no-go theorem disallowing such flux.
In the context of quantum state engineering we analyze the effect of observation on nonlinear optical $n$-photon Fock state generation. We show that it is possible to truncate the vacuum component from an arbitrary photon number superposition without modifying its remaining parts. In the course of the full dynamical analysis of the effect of observation, it is also found that the Zeno and the anti-Zeno effects repeat periodically. We discuss the close relationship between vacuum state truncation and so-called "interaction-free" measurement.
We present line-strength measurements for 74 early-type galaxies in the core of the Coma cluster reaching down to velocity dispersions, sigma, of 30 km/s. The index-sigma relations for our sample, including galaxies with sigma<100 km/s (low-sigma), differ in shape depending on which index is used. We notice two types of relations for the metallic indices: one showing a break in the slope around ~100 km/s, and another group with strong linear relations between an index and log sigma. We find no connection between the behavior of index-sigma relations with either alpha- or Fe-peak elements. However, we find indications that the relations are tighter for indices which do not depend on the micro-turbulent velocities of stellar atmospheres. We confirm previous results that low-sigma galaxies including dE/dS0s are on average younger, less metal rich, and have lower [alpha/Fe] in comparison to E/S0s. Our data show that these trends derived for high-sigma galaxies extend down to dE/dS0s. This is a factor of ~2 lower in sigma than previously published work. We confirm that the observed anti-correlation between age and metallicity for high-sigma galaxies is consistent with the effects of correlated errors. Low-sigma galaxies also show a similar relation between age and metallicity as a result of correlated errors. However, they are offset from this relationship so that, on average, they are less metal rich and younger than their high-sigma counterparts.