ShantanuT01/DACTYL-Pretraining huggingface dataset:
The crucial condition in the derivation of the Jarzynski equality (JE) from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three \textit{Gedanken} experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.
The discovery of luminous quasars at redshifts up to 7.5 demonstrates the existence of several billion M_sun supermassive black holes (SMBHs) less than a billion years after the Big Bang. They are accompanied by intense star formation in their host galaxies, pinpointing sites of massive galaxy assembly in the early universe, while their absorption spectra reveal an increasing neutral intergalactic medium (IGM) at the epoch of reionization. Extrapolating from the rapid evolution of the quasar density at z=5-7, we expect that there is only one luminous quasar powered by a billion M_sun SMBH in the entire observable universe at z~9. In the next decade, new wide-field, deep near-infrared (NIR) sky surveys will push the redshift frontier to the first luminous quasars at z~9-10; the combination with new deep X-ray surveys will probe fainter quasar populations that trace earlier phases of SMBH growth. The identification of these record-breaking quasars, and the measurements of their BH masses and accretion properties require sensitive spectroscopic observations with next generation of ground-based and space telescopes at NIR wavelengths. High-resolution integral-field spectroscopy at NIR, and observations at millimeter and radio wavelengths, will together provide a panchromatic view of the quasar host galaxies and their galactic environment at cosmic dawn, connecting SMBH growth with the rise of the earliest massive galaxies. Systematic surveys and multiwavelength follow-up observations of the earliest luminous quasars will strongly constrain the seeding and growth of the first SMBHs in the universe, and provide the best lines of sight to study the history of reionization.
The recently-computed ExoMol line lists for isotopologues of AlH are used to analyse the blue spectrum (4000-4500 {\AA}) of Proxima Cen (M5.5 V). Comparison of the observed and computed spectra enables the identification of a large number of 27AlH lines of the A1{\Pi} - X1{\Sigma}+ band system: the spectral range covering 1-0, 0-0 and 1-1 bands is dominated by clearly resolved AlH lines. We reveal the diffuse nature of transitions close to the dissociation limit which appears in the form of increasingly wider(up to 5 {\AA}) and shallower (up to the continuum confusion limit) AlH line profiles. The predicted wavelengths of AlH diffuse lines are systematically displaced. The effect broadening by pre-dissociation states on the line profiles is included by increasing the radiative damping rate by up to 5 orders of magnitude. We determine empirical values of damping rates for a number of the clean 0-0 Q-branch transitions by comparing the observed and synthetic stellar spectra. We find excellent agreement between our damping rates and lifetimes available in the literature. A comparison of 27Al1H ExoMol and REALH spectra shows that the observed spectrum is better described by the ExoMol line list. A search for 26Al1H lines in the Proxima Cen spectrum does not reveal any notable features; giving an upper limit of 27Al1H/26Al1H {>} 100.
We propose a method that learns a discriminative yet semantic space for object categorization, where we also embed auxiliary semantic entities such as supercategories and attributes. Contrary to prior work which only utilized them as side information, we explicitly embed the semantic entities into the same space where we embed categories, which enables us to represent a category as their linear combination. By exploiting such a unified model for semantics, we enforce each category to be represented by a supercategory + sparse combination of attributes, with an additional exclusive regularization to learn discriminative composition.
We give some new results on algebraic independence within Mahler's method, including algebraic independence of values at transcendental points. We also give some new measures of algebraic independence for infinite series of numbers. In particular, our results furnishes, for $n\geq 1$ arbitrarily large, new examples of sets $(\theta_1,...,\theta_n)\in\mrr^n$ normal in the sense of definition formulated by Grigory Chudnovsky (1980).
We consider the tree-reduced path of symmetric random walk on $\ZZ^{d}$. It is interesting to ask about the number of turns $T_n$ in the reduced path after $n$ steps. This question arises from inverting signature for lattice paths. We show that, when $n$ is large, the mean and variance of $T_n$ have the same order as $n$, while the second order terms are O(1). We then use these estimates to obtain limit theorems for $T_n$. Similar results hold for any other finite patterns as well.
We consider a free fermion formulation of a statistical model exhibiting a limit shape phenomenon. The model is shown to have a phase transition that can be visualized as the merger of two liquid regions - arctic circles. We show that the merging arctic circles provide a space-time resolved picture of the phase transition in lattice QCD known as Gross-Witten-Wadia transition. The latter is a continuous phase transition of the third order. We argue that this transition is universal and is not spoiled by interactions if parity and time-reversal symmetries are preserved. We refer to this universal transition as the Merger Transition.
We present new photometric data and analysis of the long-duration UBV photoelectric observations for three candidates to protoplanetary objects - F-supergiants with IR-excesses located at large galactic latitudes, IRAS 18095+2704, IRAS 19386+0155, and IRAS 19500-1709. All three stars have revealed quasiperiodic low-amplitude variabilities caused by pulsations observed against the long-term trends of brightnesses. For IRAS 18095+2704=V887 Her we have found a pulsation period of 109 days and a linear trend of brightness under the constant colours if being averaged over the year timescale. The light curve of IRAS 19386+0155=V1648 Aql over 2000-2008 can be approximated by a wave with a main period of 102 days which is modulated by close frequency, with a period of 98 days, that results in brightness oscillations with a variable amplitude. V1648 Aql has also shown synchronous reddening together with a persistent rise of brightness in the V-band. IRAS 19500-1709=V5112 Sgr experiences irregular pulsations with the periods of 39 and 47 days. The long-term component of the variability of V5112 Sgr may be related to the binary character of this star.
We propose a novel solution for semi-supervised video object segmentation. By the nature of the problem, available cues (e.g. video frame(s) with object masks) become richer with the intermediate predictions. However, the existing methods are unable to fully exploit this rich source of information. We resolve the issue by leveraging memory networks and learn to read relevant information from all available sources. In our framework, the past frames with object masks form an external memory, and the current frame as the query is segmented using the mask information in the memory. Specifically, the query and the memory are densely matched in the feature space, covering all the space-time pixel locations in a feed-forward fashion. Contrast to the previous approaches, the abundant use of the guidance information allows us to better handle the challenges such as appearance changes and occlussions. We validate our method on the latest benchmark sets and achieved the state-of-the-art performance (overall score of 79.4 on Youtube-VOS val set, J of 88.7 and 79.2 on DAVIS 2016/2017 val set respectively) while having a fast runtime (0.16 second/frame on DAVIS 2016 val set).
A classic approach toward zero-shot learning (ZSL) is to map the input domain to a set of semantically meaningful attributes that could be used later on to classify unseen classes of data (e.g. visual data). In this paper, we propose to learn a visual feature dictionary that has semantically meaningful atoms. Such dictionary is learned via joint dictionary learning for the visual domain and the attribute domain, while enforcing the same sparse coding for both dictionaries. Our novel attribute aware formulation provides an algorithmic solution to the domain shift/hubness problem in ZSL. Upon learning the joint dictionaries, images from unseen classes can be mapped into the attribute space by finding the attribute aware joint sparse representation using solely the visual data. We demonstrate that our approach provides superior or comparable performance to that of the state of the art on benchmark datasets.
Knowledge of the human visual system helps to develop better computational models of visual attention. State-of-the-art models have been developed to mimic the visual attention system of young adults that, however, largely ignore the variations that occur with age. In this paper, we investigated how visual scene processing changes with age and we propose an age-adapted framework that helps to develop a computational model that can predict saliency across different age groups. Our analysis uncovers how the explorativeness of an observer varies with age, how well saliency maps of an age group agree with fixation points of observers from the same or different age groups, and how age influences the center bias. We analyzed the eye movement behavior of 82 observers belonging to four age groups while they explored visual scenes. Explorativeness was quantified in terms of the entropy of a saliency map, and area under the curve (AUC) metrics was used to quantify the agreement analysis and the center bias. These results were used to develop age adapted saliency models. Our results suggest that the proposed age-adapted saliency model outperforms existing saliency models in predicting the regions of interest across age groups.
We show that hard encounters in the central regions of globular clusters embedded in dark matter (DM) haloes necessarily lead to the formation of gravitationally-bound stellar envelopes that extend far beyond the nominal tidal radius of the system. Using statistical arguments and numerical techniques we derive the equilibrium distribution function of stars ejected from the centre of a non-divergent spherical potential. Independently of the velocity distribution with which stars are ejected, GC envelopes have density profiles that approach asymptotically $\rho\sim r^{-4}$ at large distances and become isothermal towards the centre. Adding a DM halo component leaves two clear-cut observational signatures: (i) a flattening, or slightly increase of the projected velocity dispersion profile at large distances, and (ii) an outer surface density profile that is systematically shallower than in models with no dark matter.
New photometric observations of NSVS 01286630 were performed and two sets of four-color (B, V , Rc, Ic) light curves (LCs) were obtained. Using the 2013 version of the Wilson-Devinney (W-D) code, we analyzed these data. The photometric solutions reveal that NSVS 01286630 is an active detached eclipsing binary (EB) with a high orbit inclination. Remarkably, the temperature of the primary component (the hotter star) is higher than the secondary one, but, the value of mass ratio q(M2/M1) for NSVS 0128663 is more than 1, which can be explained that the surface of the secondary component of NSVS 01286630 is covered with big cool-star-spots. Based on our new CCD mid-eclipse times and the data published until now, the variations of the mid-eclipse times were reanalyzed in detail using a weighted least-squares method. It is discovered that the (O-C) diagram of the system shows a cyclic oscillation with a period of 3.61 yr and an amplitude of 0.001 days. The cyclic variation may be caused by the light travel time effect (LTTE) due to the presence of a third companion, whose mass we calculated is about 0.11 solar mass. The third body may affect the orbital evolution of the central binary system by transferring the angular momentum.
In this paper, we propose an easily trained yet powerful representation learning approach with performance highly competitive to deep neural networks in a digital pathology image segmentation task. The method, called sparse coding driven deep decision tree ensembles that we abbreviate as ScD2TE, provides a new perspective on representation learning. We explore the possibility of stacking several layers based on non-differentiable pairwise modules and generate a densely concatenated architecture holding the characteristics of feature map reuse and end-to-end dense learning. Under this architecture, fast convolutional sparse coding is used to extract multi-level features from the output of each layer. In this way, rich image appearance models together with more contextual information are integrated by learning a series of decision tree ensembles. The appearance and the high-level context features of all the previous layers are seamlessly combined by concatenating them to feed-forward as input, which in turn makes the outputs of subsequent layers more accurate and the whole model efficient to train. Compared with deep neural networks, our proposed ScD2TE does not require back-propagation computation and depends on less hyper-parameters. ScD2TE is able to achieve a fast end-to-end pixel-wise training in a layer-wise manner. We demonstrated the superiority of our segmentation technique by evaluating it on the multi-disease state and multi-organ dataset where consistently higher performances were obtained for comparison against several state-of-the-art deep learning methods such as convolutional neural networks (CNN), fully convolutional networks (FCN), etc.
We show that birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth minimal models share the same Betti numbers. Our methods indicate a link between $p$-adic measure and the minimal model theory.
We use direct Kaluza-Klein reduction to calculate the spectrum of spin-2 modes around a warped product of AdS_4 and a certain squashed and stretched 7-sphere. The modes turn out to be polynomials in the four complex variables parameterizing the sphere, and their complex conjugates. The background, which possesses U(1)_R x SU(3) symmetry, has been conjectured to be dual to a U(N) x U(N) N=2 superconformal Chern-Simons theory with a sextic superpotential. We find that the U(1)_R x SU(3) quantum numbers of spin-2 modes are in agreement with those determined in arXiv:0809.3773 through a group theoretic method, and with the spectrum of spin-2 gauge invariant operators in the Chern-Simons gauge theory. The mass-squared in AdS_4 is found to be quadratic in these quantum numbers and the Kaluza-Klein excitation number. Most of the spin-2 operators belong to long multiplets, and we determine their dimensions via the AdS/CFT correspondence.
For integers $m_1,...,m_d>0$ and a cuboid $M=[0,m_1]\times ... \times [0,m_d]\subset \mathbb{R}^d$, a brick of $M$ is a closed cuboid whose vertices have integer coordinates. A set $H$ of bricks in $M$ is a system of brick islands if for each pair of bricks in $H$ one contains the other or they are disjoint. Such a system is maximal if it cannot be extended to a larger system of brick islands. Extending the work of Lengv\'{a}rszky, we show that the minimum size of a maximal system of brick islands in $M$ is $\sum_{i=1}^d m_i - (d-1)$. Also, in a cube $C=[0,m]^d$ we define the corresponding notion of a system of cubic islands, and prove bounds on the sizes of maximal systems of cubic islands.
The regular independence number, introduced by Albertson and Boutin in 1990, is the size of a largest set of independent vertices with the same degree. Lower bounds were proven for this invariant, in terms of the order, for trees and planar graphs. In this article, we generalize and extend these results to find lower bounds for the regular $k$-independence number for trees, forests, planar graphs, $k$-trees and $k$-degenerate graphs.
Wormhole solutions in classical General Relativity are unstable and hence non traversable. Morris and Thorne discovered a traversable wormhole solution that required the energy momentum tensor of matter sources to violate various energy conditions and are out of the purview of the standard model of particle physics. The search for traversable wormhole solutions in Modified Theories of Gravity has been of significant interest in the decades after Morris and Thorne first published their results as such violations may be avoided in such theories. This work comprehensively reviews traversable wormhole solutions in modified theories of gravity with extra dimensions that satisfy the various energy conditions with an in depth look at the matter sources and the various constraints on the parameters of the theory to make the energy momentum of the matter sources respect the energy conditions.
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and simulations of a tagged particle moving on a two-dimensional periodic potential energy surface, both in the presence and absence of noise. Langevin dynamics simulations at multiple temperatures are carried out to obtain the diffusion coefficient of a solute particle. Friction is varied from zero to large values. Diffusive motion emerges in the limit of long times, even in the absence of noise, although the trajectory is found to remain correlated over a long time. This correlation is manifested in correlated returns to the starting minima following a scattering by surrounding maxima. Noise destroys this correlation, induces chaos, and increases diffusion at small friction. Diffusion thus exhibits a non-monotonic friction dependence at the intermediate value of the damping, ultimately converging to our theoretically predicted value. The latter is obtained by using the well-established relation between diffusion and random walk. An excellent agreement is obtained between theory and simulations in the high friction limit, but not so in the intermediate regime. The rate of escape from one cell to another is obtained from the multidimensional rate theory of Langer. We find that enhanced dimensionality plays an important role. In order to quantify the effects of noise on the potential-imposed coherence on the trajectories, we calculate the Lyapunov exponent. At small friction values, the Lyapunov exponent mimics the friction dependence of the rate.
We demonstrate double quantum dots fabricated in undoped Si/SiGe heterostructures relying on a double top-gated design. Charge sensing shows that we can reliably deplete these devices to zero charge occupancy. Measurements and simulations confirm that the energetics are determined by the gate-induced electrostatic potentials. Pauli spin blockade has been observed via transport through the double dot in the two electron configuration, a critical step in performing coherent spin manipulations in Si.
Usage of the Thomas-Ehrman Level Displacement formalism has been examined. Mistakes and inconsistencies are found in several papers, being repeated in subsequent works. Here, we present a complete formalism with a consistent set of definitions. Full algorithms are made available, both as a {\tt FORTRAN} source file and as a user-friendly Visual Basic executable tool, available for download on the World Wide Web.
For any integer $x$, let $T_x$ denote the triangular number $\frac{x(x+1)}{2}$. In this paper we give a complete characterization of all the triples of positive integers $(\alpha, \beta, \gamma)$ for which the ternary sums $\alpha x^2 +\beta T_y + \gamma T_z$ represent all but finitely many positive integers. This resolves a conjecture of Kane and Sun \cite[Conjecture 1.19(i)]{KS08} and complete the characterization of all almost universal ternary mixed sums of squares and triangular numbers.
Surface-brightness profiles for early-type (S0-Sb) disks exhibit three main classes (Type I, II, and III). Type II profiles are more common in barred galaxies, and most of the time appear to be related to the bar's Outer Lindblad Resonance. Roughly half of barred galaxies in the field have Type II profiles, but almost none in the Virgo Cluster do; this might be related to ram-pressure stripping in clusters. A strong \textit{anti}correlation is found between Type III profiles ("antitruncations") and bars: Type III profiles are most common when there is no bar, and least common when there is a strong bar.
A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question which moves in the class can be adjoined without changing the winning strategy of nim. The results apply to other combinatorial games with unbounded Sprague-Grundy function values. We formulate two weakened conditions of the notion of nim-sum 0 for proving the results.
We present two kinds of acoustic models for the massless electric charge conceived by Einstein and Rosen in the form of a bridge (wormhole throat). It is found that the first kind of modelling requires a thin layer of exotic matter at the bridge. We also derive an acoustic equation that exclusively characterizes the model. Using a second kind of model, it is demonstrated that the Einstein-Rosen charge has a sonic Hawking-Unruh temperature proportional to +-1/$beta$, where $beta$ is the size of the charge. This suggests that (squealing!) wormholes can also be formally accommodated into Unruh's fluid model.
We consider a random walk with catastrophes which was introduced to model population biology. It is known that this Markov chain gets eventually absorbed at $0$ for all parameter values. Recently, it has been shown that this chain exhibits a metastable behavior in the sense that it can persist for a very long time before getting absorbed. In this paper we study this metastable phase by making the parameters converge to extreme values. We obtain four different limits that we believe shed light on the metastable phase.
We recently initiated a search for ultra-compact dwarf galaxies (UCDs) in the Centaurus galaxy cluster (Mieske et al. 2007), resulting in the discovery of 27 compact objects with -12.2<M_V<-10.9 mag. Our overall survey completeness was 15-20% within 120 kpc projected clustercentric distance. In order to better constrain the luminosity distribution of the brightest UCDs in Centaurus, we continue our search by substantially improving our survey completeness specifically in the regime M_V<-12 mag (V_0<21.3 mag). Using VIMOS at the VLT, we obtain low-resolution spectra of 400 compact objects with 19.3<V_0<21.3 mag (-14<M_V<-12 mag at the Centaurus distance) in the central 25' of the Centaurus cluster, which corresponds to a projected radius of ~150 kpc. Our survey yields complete area coverage within ~120 kpc. For 94% of the sources included in the masks we successfully measure a redshift. Due to incompleteness in the slit assignment, our final completeness in the area surveyed is 52%. Among our targets we find three new UCDs in the magnitude range -12.2<M_V<-12 mag, hence at the faint limit of our survey. One of them is covered by archival HST WFPC2 imaging, yielding a size estimate of r_h <= 8-9 pc. At 95% confidence we can reject the hypothesis that in the area surveyed there are more than 2 massive UCDs with M_V<-12.2 mag and r_eff <=70 pc. Our survey hence confirms the extreme rareness of massive UCDs. We find that the radial distributions of Centaurus and Fornax UCDs with respect to their host clusters' centers agree within the 2 sigma level.