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the bitcoin cryptocurrency records its transactions in a public log called the blockchain. its security rests critically on the distributed protocol that maintains the blockchain, run by participants called miners. conventional wisdom asserts that the protocol is incentive - compatible and secure against colluding minority groups, i. e., it incentivizes miners to follow the protocol as prescribed. we show that the bitcoin protocol is not incentive - compatible. we present an attack with which colluding miners obtain a revenue larger than their fair share. this attack can have significant consequences for bitcoin : rational miners will prefer to join the selfish miners, and the colluding group will increase in size until it becomes a majority. at this point, the bitcoin system ceases to be a decentralized currency. selfish mining is feasible for any group size of colluding miners. we propose a practical modification to the bitcoin protocol that protects against selfish mining pools that command less than 1 / 4 of the resources. this threshold is lower than the wrongly assumed 1 / 2 bound, but better than the current reality where a group of any size can compromise the system. | arxiv:1311.0243 |
we study the sensitivity of top pair production at the large hadron collider ( lhc ) to the nature of an underlying z ' boson, including full tree level standard model background effects and interferences while assuming realistic final state reconstruction efficiencies. we demonstrate that exploiting asymmetry observables represents a promising way to distinguish between a selection of benchmark z ' models due to their unique dependences on the chiral couplings of the new gauge boson | arxiv:1211.5470 |
the motility of microorganisms is influenced greatly by their hydrodynamic interactions with the fluidic environment they inhabit. we show by direct experimental observation of the bi - flagellated alga chlamydomonas reinhardtii that fluid elasticity and viscosity strongly influence the beating pattern - the gait - and thereby control the propulsion speed. the beating frequency and the wave speed characterizing the cyclical bending are both enhanced by fluid elasticity. despite these enhancements, the net swimming speed of the alga is hindered for fluids that are sufficiently elastic. the origin of this complex response lies in the interplay between the elasticity - induced changes in the spatial and temporal aspects of the flagellar cycle and the buildup and subsequent relaxation of elastic stresses during the power and recovery strokes. | arxiv:1511.00662 |
utilizing a qcd coulomb gauge hamiltonian with linear confinement specified by lattice, we report a relativistic many - body calculation for the light exotic and charmed hybrid mesons. the hamiltonian successfully describes both quark and gluon sectors, with vacuum and quasiparticle properties generated by a bcs transformation and more elaborate tda and rpa diagonalizations for the meson ( $ q \ bar { q } $ ) and glueball ( $ gg $ ) masses. hybrids entail a computationally intense relativistic three quasiparticle ( $ q \ bar { q } g $ ) calculation with the 9 dimensional hamiltonian matrix elements evaluated variationally by monte carlo techniques. our new tda ( rpa ) spectrum for the nonexotic $ 1 ^ { - - } $ charmed ( $ c \ bar { c } $ and $ c \ bar { c } g $ ) system provides an explanation for the overpopulation of the observed $ j / \ psi $ states. for the important $ 1 ^ { - + } $ light exotic channel we obtain hybrid masses above 2 $ gev $, in broad agreement with lattice and flux tube models, indicating that the recently observed resonances at 1. 4 and 1. 6 $ gev $ are of different, perhaps four quark, structure. | arxiv:hep-ph/0008337 |
of living cell suspensions in set high - resolution patterns. the investigation was successful, the researchers foresee that " generated tissue constructs might be used for in vivo testing by implanting them into animal models " ( 14 ). as of this study, only human skin tissue has been synthesized, though researchers project that " by integrating further cell types ( e. g. melanocytes, schwann cells, hair follicle cells ) into the printed cell construct, the behavior of these cells in a 3d in vitro microenvironment similar to their natural one can be analyzed ", which is useful for drug discovery and toxicology studies. = = = = self - assembled recombinant spider silk nanomembranes = = = = gustafsson et al. demonstrated free ‐ standing, bioactive membranes of cm - sized area, but only 250 nm thin, that were formed by self ‐ assembly of spider silk at the interface of an aqueous solution. the membranes uniquely combine nanoscale thickness, biodegradability, ultrahigh strain and strength, permeability to proteins and promote rapid cell adherence and proliferation. they demonstrated growing a coherent layer of keratinocytes. these spider silk nanomembranes have also been used to create a static in - vitro model of a blood vessel. = = = = tissue engineering in situ = = = = in situ tissue regeneration is defined as the implantation of biomaterials ( alone or in combination with cells and / or biomolecules ) into the tissue defect, using the surrounding microenvironment of the organism as a natural bioreactor. this approach has found application in bone regeneration, allowing the formation of cell - seeded constructs directly in the operating room. = = assembly methods = = a persistent problem within tissue engineering is mass transport limitations. engineered tissues generally lack an initial blood supply, thus making it difficult for any implanted cells to obtain sufficient oxygen and nutrients to survive, or function properly. = = = self - assembly = = = self - assembly methods have been shown to be promising methods for tissue engineering. self - assembly methods have the advantage of allowing tissues to develop their own extracellular matrix, resulting in tissue that better recapitulates biochemical and biomechanical properties of native tissue. self - assembling engineered articular cartilage was introduced by jerry hu and kyriacos a. athanasiou in 2006 and applications of the process have resulted in engineered cartilage approaching | https://en.wikipedia.org/wiki/Tissue_engineering |
volumetric ( 4d ) performance capture is fundamental for ar / vr content generation. whereas previous work in 4d performance capture has shown impressive results in studio settings, the technology is still far from being accessible to a typical consumer who, at best, might own a single rgbd sensor. thus, in this work, we propose a method to synthesize free viewpoint renderings using a single rgbd camera. the key insight is to leverage previously seen " calibration " images of a given user to extrapolate what should be rendered in a novel viewpoint from the data available in the sensor. given these past observations from multiple viewpoints, and the current rgbd image from a fixed view, we propose an end - to - end framework that fuses both these data sources to generate novel renderings of the performer. we demonstrate that the method can produce high fidelity images, and handle extreme changes in subject pose and camera viewpoints. we also show that the system generalizes to performers not seen in the training data. we run exhaustive experiments demonstrating the effectiveness of the proposed semi - parametric model ( i. e. calibration images available to the neural network ) compared to other state of the art machine learned solutions. further, we compare the method with more traditional pipelines that employ multi - view capture. we show that our framework is able to achieve compelling results, with substantially less infrastructure than previously required. | arxiv:1905.12162 |
we investigate how elimination of variables can affect the asymptotic dynamics and phenotype control of boolean networks. in particular, we look at the impact on minimal trap spaces, and identify a structural condition that guarantees their preservation. we examine the possible effects of variable elimination under three of the most popular approaches to control ( attractor - based control, value propagation and control of minimal trap spaces ), and under different update schemes ( synchronous, asynchronous, generalized asynchronous ). we provide some insights on the application of reduction, and an ample inventory of examples and counterexamples. | arxiv:2406.02304 |
in loop quantum gravity mathematically rigorous models of full quantum gravity were proposed. in this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to massless scalar field. in our previous research we introduced a method to reduce the model to homogeneous - isotropic sector at the quantum level. in this paper we propose a method to restrict to the spatially flat sector. after this restriction the number of degrees of freedom gets substantially reduced. this allows us to make numerical calculations. remarkably, the resulting model shares some structural similarities with the loop quantum cosmological models and therefore sheds some new light on the relation between loop quantum gravity and loop quantum cosmology. according to our model the evolution of the universe is periodic. the quantum gravity effects resolve the big bang singularity leading to a big bounce and cause the universe to contract after a classical expansion phase ( big crunch ). | arxiv:2211.04440 |
we study a stackelberg game between a base station and a multi - antenna power beacon for wireless energy harvesting in a multiple sensor node scenario. assuming imperfect csi between the sensor nodes and the power beacon, we propose a utility function that is based on throughput non - outage probability at the base station. we provide an analytical solution for the equilibrium in case of a single sensor node. for the general case consisting of multiple sensor nodes, we provide upper and lower bounds on the power and price ( players ' strategies ). we compare the bounds with solutions resulting from an exhaustive search and a relaxed semidefinite program, and find the upper bound to be tight. | arxiv:1605.02330 |
the problem of finding a rank - one solution to a system of linear matrix equations arises from many practical applications. given a system of linear matrix equations, however, such a low - rank solution does not always exist. in this paper, we aim at developing some sufficient conditions for the existence of a rank - one solution to the system of homogeneous linear matrix equations ( hlme ) over the positive semidefinite cone. first, we prove that an existence condition of a rank - one solution can be established by a homotopy invariance theorem. the derived condition is closely related to the so - called $ p _ \ emptyset $ property of the function defined by quadratic transformations. second, we prove that the existence condition for a rank - one solution can be also established through the maximum rank of the ( positive semidefinite ) linear combination of given matrices. it is shown that an upper bound for the rank of the solution to a system of hlme over the positive semidefinite cone can be obtained efficiently by solving a semidefinite programming ( sdp ) problem. moreover, a sufficient condition for the nonexistence of a rank - one solution to the system of hlme is also established in this paper. | arxiv:1211.2131 |
we present the results of a transcontinental campaign to observe the 2009 june 5 transit of the exoplanet hd 80606b. we report the first detection of the transit ingress, revealing the transit duration to be 11. 64 + / - 0. 25 hr and allowing more robust determinations of the system parameters. keck spectra obtained at midtransit exhibit an anomalous blueshift, giving definitive evidence that the stellar spin axis and planetary orbital axis are misaligned. the keck data show that the projected spin - orbit angle is between 32 - 87 deg with 68. 3 % confidence and between 14 - 142 deg with 99. 73 % confidence. thus the orbit of this planet is not only highly eccentric ( e = 0. 93 ), but is also tilted away from the equatorial plane of its parent star. a large tilt had been predicted, based on the idea that the planet ' s eccentric orbit was caused by the kozai mechanism. independently of the theory, it is noteworthy that all 3 exoplanetary systems with known spin - orbit misalignments have massive planets on eccentric orbits, suggesting that those systems migrate differently than lower - mass planets on circular orbits. | arxiv:0907.5205 |
given two martingales on the filtration generated by two dimensional brownian motion, we want to estimate the $ l ^ p $ norm of the subordinated one if we have some extra orthogonality property available. we construct several new bellman functions, very different from burkholder ' s function, and using them give an estimate of $ l ^ p $ norm of a subordinated martingale, if the dominating martingale is orthogonal and $ 1 < p \ le 2 $. we use monge - - ampere equation to construct these bellman functions. | arxiv:1012.0947 |
the dynamic analysis of structural change in the organization of the sciences requires methodologically the integration of multivariate and time - series analysis. structural change - - e. g., interdisciplinary development - - is often an objective of government interventions. recent developments in multi - dimensional scaling ( mds ) enable us to distinguish the stress originating in each time - slice from the stress originating from the sequencing of time - slices, and thus to locally optimize the trade - offs between these two sources of variance in the animation. furthermore, visualization programs like pajek and visone allow us to show not only the positions of the nodes, but also their relational attributes like betweenness centrality. betweenness centrality in the vector space can be considered as an indicator of interdisciplinarity. using this indicator, the dynamics of the citation impact environments of the journals cognitive science, social networks, and nanotechnology are animated and assessed in terms of interdisciplinarity among the disciplines involved. | arxiv:0911.1437 |
in 2009 lurie published an expository article outlining a proof for a higher version of the cobordism hypothesis conjectured by baez and dolan in 1995. in this note we give a proof for the 1 - dimensional case of this conjecture. the proof follows most of the outline given in lurie ' s paper, but differs in a few crucial details. in particular, the proof makes use of the theory of quasi - unital $ \ infty $ - categories as developed by the author in a previous note. | arxiv:1210.0229 |
in this work, we are concerned with maximizing the lifetime of a cluster of sensors engaged in single - hop communication with a base - station. in a data - gathering network, the spatio - temporal correlation in sensor data induces data - redundancy. also, the interaction between two communicating parties is well - known to reduce the communication complexity. this paper proposes a formalism that exploits these two opportunities to reduce the number of bits transmitted by a sensor node in a cluster, hence enhancing its lifetime. we argue that our approach has several inherent advantages in scenarios where the sensor nodes are acutely energy and computing - power constrained, but the base - station is not so. this provides us an opportunity to develop communication protocols, where most of the computing and communication is done by the base - station. the proposed framework casts the sensor nodes and base - station communication problem as the problem of multiple informants with correlated information communicating with a recipient and attempts to extend extant work on interactive communication between an informant - recipient pair to such scenarios. our work makes four major contributions. firstly, we explicitly show that in such scenarios interaction can help in reducing the communication complexity. secondly, we show that the order in which the informants communicate with the recipient may determine the communication complexity. thirdly, we provide the framework to compute the $ m $ - message communication complexity in such scenarios. lastly, we prove that in a typical sensor network scenario, the proposed formalism significantly reduces the communication and computational complexities. | arxiv:cs/0701048 |
the black hole at the galactic center, sgr a *, is the prototype of a galactic nucleus at a very low level of activity. its radio through submm - wave emission is known to come from a region close to the event horizon, however, the source of the emission is still under debate. a successful theory explaining the emission is based on a relativistic jet model scaled down from powerful quasars. we want to test the predictive power of this established jet model against newly available measurements of wavelength - dependent time lags and the size - wavelength structure in sgr a *. using all available closure amplitude vlbi data from different groups, we again derived the intrinsic wavelength - dependent size of sgr a *. this allowed us to calculate the expected frequency - dependent time lags of radio flares, assuming a range of in - and outflow velocities. moreover, we calculated the time lags expected in the previously published pressure - driven jet model. the predicted lags are then compared to radio monitoring observations at 22, 43, and 350 ghz. the combination of time lags and size measurements imply a mildly relativistic outflow with bulk outflow speeds of gamma * beta ~ 0. 5 - 2. the newly measured time lags are reproduced well by the jet model without any major fine tuning. the results further strengthen the case for the cm - to - mm wave radio emission in sgr a * as coming from a mildly relativistic jet - like outflow. the combination of radio time lag and vlbi closure amplitude measurements is a powerful new tool for assessing the flow speed and direction in sgr a *. future vlbi and time lag measurements over a range of wavelengths will reveal more information about sgr a *, such as the existence of a jet nozzle, and measure the detailed velocity structure of a relativistic jet near its launching point for the first time. | arxiv:0901.3723 |
we prove that the action of a generalized braid group on an enhanced triangulated categories, generated by spherical twist functors along an ade - configuration of $ \ omega $ - spherical objects, is faithful for any integer $ \ omega \ neq 1 $. | arxiv:1910.02401 |
the field of particle physics is living very exciting times with a plethora of experiments looking for new physics in complementary ways. this has made increasingly necessary to obtain precise predictions in new physics models in order to be ready for a discovery that might be just around the corner. however, analyzing new models and studying their phenomenology can be really challenging. computing mass matrices, interaction vertices and decay rates is already a tremendous task. in addition, obtaining predictions for the dark matter relic density and its detection prospects, computing flavor observables or estimating the lhc reach in certain collider signals constitutes quite a technical work due to the precision level that is currently required. for this reason, computer tools such as sarah, micromegas, madgraph, spheno or flavorkit have become quite popular, and many physicists use them on a daily basis. in this course we will learn how to use these computer tools to explore new physics models and get robust numerical predictions to probe them in current and future experiments. | arxiv:1507.06349 |
we propose an efficient numerical algorithm for solving integral equations of the theory of liquids in the reference interaction site model ( rism ) approximation for infinitely dilute solution of macromolecules with a large number of atoms. the algorithm is based on applying the nonstationary iterative methods for solving systems of linear algebraic equations. we calculate the solvent - solute atom - atom correlation functions for a fragment of the b - dna duplex d ( ggggg ). d ( ccccc ) in infinitely dilute aqueous solution. the obtained results are compared with available experimental data and results from computer simulations. | arxiv:cond-mat/9804176 |
we present the first application of data - driven techniques for dynamical system analysis based on koopman theory to variable stars. we focus on light curves of rrlyrae type variables, in the galactic globular cluster $ \ omega $ centauri. light curves are thus summarized by a handful of complex eigenvalues, corresponding to oscillatory or fading dynamical modes. we find that variable stars of the rrc subclass can be summarized in terms of fewer ( $ \ approx 8 $ ) eigenvalues, while rrab need comparatively more ( $ \ approx 12 $ ). this result can be leveraged for classification and reflects the simpler structure of rrc light curves. we then consider variable stars displaying secular variations due to the tseraskaya - blazhko effect and find a change in relevant eigenvalues with time, with possible implications for the physical interpretation of the effect. | arxiv:2407.16868 |
the following paper presents a systematic 3rd generation partnership project ( 3gpp ) - compliant characterization of radar cross section ( rcs ) for indoor factory ( inf ) objects, including small and mid - sized unmanned aerial vehicles ( uavs ), robotic arms, and automated guided vehicles ( agvs ). through measurements in the 25 - 28 ghz range, we validate the 3gpp standardized log - normal distribution model for rcs for above - mentioned target objects. the 3gpp - complaint rcs parameters obtained for the small - sized uav are in close agreement ( < 1 db deviation ) with 3gpp agreed values. the mid - sized uavs exhibit higher reflectivity compared to the small - sized uav due to enhanced specular components attributed to material and lithium - ion battery packs. the robotic arm exhibits dynamic rcs behavior due to mechanical articulation, whereas uavs show clear size - dependent reflectivity patterns in agvs. our findings provide empirical validation for rcs characterization for integrated sensing and communication channel modeling in inf environments. | arxiv:2505.08754 |
the official investigation into the collapse of the world trade center buildings. following the 2021 surfside condominium building collapse, nist sent engineers to the site to investigate the cause of the collapse. in 2019, nist launched a program named nist on a chip to decrease the size of instruments from lab machines to chip size. applications include aircraft testing, communication with satellites for navigation purposes, and temperature and pressure. in 2023, the biden administration began plans to create a u. s. ai safety institute within nist to coordinate ai safety matters. according to the washington post, nist is considered " notoriously underfunded and understaffed ", which could present an obstacle to these efforts. = = constitution = = nist, known between 1901 and 1988 as the national bureau of standards ( nbs ), is a measurement standards laboratory, also known as the national metrological institute ( nmi ), which is a non - regulatory agency of the united states department of commerce. the institute ' s official mission is to : promote u. s. innovation and industrial competitiveness by advancing measurement science, standards, and technology in ways that enhance economic security and improve our quality of life. nist had an operating budget for fiscal year 2007 ( october 1, 2006 – september 30, 2007 ) of about $ 843. 3 million. nist ' s 2009 budget was $ 992 million, and it also received $ 610 million as part of the american recovery and reinvestment act. nist employs about 2, 900 scientists, engineers, technicians, and support and administrative personnel. about 1, 800 nist associates ( guest researchers and engineers from american companies and foreign countries ) complement the staff. in addition, nist partners with 1, 400 manufacturing specialists and staff at nearly 350 affiliated centers around the country. nist publishes the handbook 44 that provides the " specifications, tolerances, and other technical requirements for weighing and measuring devices ". = = = metric system = = = the congress of 1866 made use of the metric system in commerce a legally protected activity through the passage of metric act of 1866. on may 20, 1875, 17 out of 20 countries signed a document known as the metric convention or the treaty of the meter, which established the international bureau of weights and measures under the control of an international committee elected by the general conference on weights and measures. = = organization = = nist is headquartered in gaithersburg, maryland, and operates a facility in boulder, colorado, which was dedicated by president eisenhower in 1954. | https://en.wikipedia.org/wiki/National_Institute_of_Standards_and_Technology |
optical power measurements are needed in practically all technologies based on light. here we report a general - purpose optical power detector based on the photoacoustic effect. optical power incident on the detector ' s black absorber produces an acoustic signal, which is further converted into an electrical signal using a silicon - cantilever pressure transducer. we demonstrate an exceptionally large spectral coverage from ultraviolet to far infrared, with the possibility for further extension to the terahertz region. the linear dynamic range of the detector reaches 80 db, ranging from a noise - equivalent power of 6 nw to 600 mw. | arxiv:2104.06930 |
in order to study the structure of $ a ^ + ( b _ n ) $ - - the affine near - semiring over a brandt semigroup - - this work completely characterizes the green ' s classes of its semigroup reducts. in this connection, this work characterizes the elements of $ a ^ + ( b _ n ) $ and reports the size of $ a ^ + ( b _ n ) $. further, idempotents and regular elements of the semigroup reducts of $ a ^ + ( b _ n ) $ have also been characterized and studied some relevant semigroups in $ a ^ + ( b _ n ) $. | arxiv:1301.6438 |
we test the performances of two different approaches to the computation of forces for molecular dynamics simulations on graphics processing units. a " vertex - based " approach, where a computing thread is started per particle, is compared to a newly proposed " edge - based " approach, where a thread is started per each potentially non - zero interaction. we find that the former is more efficient for systems with many simple interactions per particle, while the latter is more efficient if the system has more complicated interactions or fewer of them. by comparing computation times on more and less recent gpu technology, we predict that, if the current trend of increasing the number of processing cores - as opposed to their computing power - remains, the " edge - based " approach will gradually become the most efficient choice in an increasing number of cases. | arxiv:1401.4350 |
we reconsider the options for cosmological holography. we suggest that a global and time - - symmetric version of the fischler - susskind bound is the most natural generalization of the holographic bound encountered in ads and de sitter space. a consistent discussion of cosmological holography seems to imply an understanding of the notion of ` ` number of degrees of freedom ' ' that deviates from its simple definition as the entropy of the current state. the introduction of a more adequate notion of degree of freedom makes the suggested variation of the fischler - susskind bound look like a stringent and viable bound in all 4 - - dimensional cosmologies without a cosmological constant. | arxiv:hep-th/9907115 |
this paper deals with a numerical analysis of plastic deformation under various conditions, utilizing radial basis function ( rbf ) approximation. the focus is on the elasto - plastic von mises problem under plane - strain assumption. elastic deformation is modelled using the navier - cauchy equation. in regions where the von mises stress surpasses the yield stress, corrections are applied locally through a return mapping algorithm. the non - linear deformation problem in the plastic domain is solved using the picard iteration. the solutions for the navier - cauchy equation are computed using the radial basis function - generated finite differences ( rbf - fd ) meshless method using only scattered nodes in a strong form. verification of the method is performed through the analysis of an internally pressurized thick - walled cylinder subjected to varying loading conditions. these conditions induce states of elastic expansion, perfectly - plastic yielding, and plastic yielding with linear hardening. the results are benchmarked against analytical solutions and traditional finite element method ( fem ) solutions. the paper also showcases the robustness of this approach by solving case of thick - walled cylinder with cut - outs. the results affirm that the rbf - fd method produces results comparable to those obtained through fem, while offering substantial benefits in managing complex geometries without the necessity for conventional meshing, along with other benefits of meshless methods. | arxiv:2405.04970 |
we give a new proof of the dilogarithm identities, associated to the ( 2, 2n + 1 ) minimal models of the virasoro algebra. | arxiv:hep-th/9212094 |
the ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. a great deal of theoretical algorithmic development has been performed in support of this goal. most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. the two most commonly used techniques for this are the jordan - wigner transformation and the bravyi - kitaev transformation. however, comparisons of these schemes have previously been limited to individual small molecules. in this paper we discuss resource implications for the use of the bravyi - kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. we consider both small systems which may be simulatable on near - future quantum devices, and systems sufficiently large for classical simulation to be intractable. we use 86 molecular systems to demonstrate that the use of the bravyi - kitaev transformation is typically at least approximately as efficient as the canonical jordan - wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations. | arxiv:1812.02233 |
we consider the magnetic interaction of exoplanets orbiting m - dwarfs, calculating the expected poynting flux carried upstream along alfv \ ' { e } n wings to the central star. a region of emission analogous to the io footprint observed in jupiter ' s aurora is produced, and we calculate the radio flux density generated near the surface of the star via the electron - cyclotron maser instability. we apply the model to produce individual case studies for the trappist - 1, proxima centauri, and the dwarf ngts - 1 systems. we predict steady - state flux densities of up to ~ 10 $ \ mu $ jy and sporadic bursts of emission of up to ~ 1 mjy from each case study, suggesting these systems may be detectable with the very large array ( vla ) and the giant metrewave radio telescope ( gmrt ), and in future with the square kilometre array ( ska ). finally, we present a survey of 85 exoplanets orbiting m - dwarfs, identifying 11 such objects capable of generating radio emission above 10 $ \ mu $ jy. | arxiv:1801.01324 |
the observation of low energy edge photoluminescence and its beneficial effect on the solar cell efficiency of ruddlesden - popper perovskites has unleashed an intensive research effort to reveal its origin. this effort, however, has been met with more challenges as the underlying material structure has still not been identified ; new modellings and observations also do not seem to converge. using 2d ( ba ) 2 ( ma ) 2pb3br10 as an example, we show that 3d mapbbr3 is formed due to the loss of ba on the edge. this self - formed mapbbr3 can explain the reported edge emission under various conditions, while the reported intriguing optoelectronic properties such as fast exciton trapping from the interior 2d perovskite, rapid exciton dissociation and long carrier lifetime can be understood via the self - formed 2d / 3d lateral perovskite heterostructure. the 3d perovskite is identified by submicron infrared spectroscopy, the emergence of xrd signature from freezer - milled nanometer - sized 2d perovskite and its photoluminescence response to external hydrostatic pressure. the revelation of this edge emission mystery and the identification of a self - formed 2d / 3d heterostructure provide a new approach to engineering 2d perovskites for high - performance optoelectronic devices. | arxiv:2001.09477 |
in this paper, we consider a global wellposed problem for the 3 - d incompressible anisotropic navier - stokes equations ( \ textit { ans } ). in order to do so, we first introduce the scaling invariant besov - sobolev type spaces, $ b ^ { - 1 + \ frac { 2 } { p }, { 1 / 2 } } _ { p } $ and $ b ^ { - 1 + \ frac { 2 } { p }, { 1 / 2 } } _ { p } ( t ) $, $ p \ geq2 $. then, we prove the global wellposedness for ( \ textit { ans } ) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $ b ^ { - 1 + \ frac { 2 } { p }, { 1 / 2 } } _ { p } $ norm. in particular, our results imply the global wellposedness of ( \ textit { ans } ) with high oscillatory initial data. | arxiv:0712.2652 |
we compute seidel ' s mirror map for abelian varieties by constructing the homogeneous coordinate rings from the fukaya category of the symplectic mirrors. the computations are feasible as only linear holomorphic disks contribute to the fukaya composition in the case of the planar lagrangians used. the map depends on a symplectomorphism $ \ rho $ representing the large complex structure monodromy. for the example of the two - torus, different families of elliptic curves are obtained by using different $ \ rho $ which are linear in the universal cover. in the case where $ \ rho $ is merely affine linear in the universal cover, the commutative elliptic curve mirror is embedded in noncommutative projective space. the case of kummer surfaces is also considered. | arxiv:math/0512229 |
a phoneme - retrieval technique is proposed, which is due to the particular way of the construction of the network. an initial set of neurons is given. the number of these neurons is approximately equal to the number of typical structures of the data. for example if the network is built for voice retrieval then the number of neurons must be equal to the number of characteristic phonemes of the alphabet of the language spoken by the social group to which the particular person belongs. usually this task is very complicated and the network can depend critically on the samples used for the learning. if the network is built for image retrieval then it works only if the data to be retrieved belong to a particular set of images. if the network is built for voice recognition it works only for some particular set of words. a typical example is the words used for the flight of airplanes. for example a command like the " airplane should make a turn of 120 degrees towards the east " can be easily recognized by the network if a suitable learning procedure is used. | arxiv:2307.07407 |
surrogate modeling is of great practical significance for parametric differential equation systems. in contrast to classical numerical methods, using physics - informed deep learning methods to construct simulators for such systems is a promising direction due to its potential to handle high dimensionality, which requires minimizing a loss over a training set of random samples. however, the random samples introduce statistical errors, which may become the dominant errors for the approximation of low - regularity and high - dimensional problems. in this work, we present a deep adaptive sampling method for surrogate modeling ( $ \ text { das } ^ 2 $ ), where we generalize the deep adaptive sampling ( das ) method [ 62 ] [ tang, wan and yang, 2023 ] to build surrogate models for low - regularity parametric differential equations. in the parametric setting, the residual loss function can be regarded as an unnormalized probability density function ( pdf ) of the spatial and parametric variables. this pdf is approximated by a deep generative model, from which new samples are generated and added to the training set. since the new samples match the residual - induced distribution, the refined training set can further reduce the statistical error in the current approximate solution. we demonstrate the effectiveness of $ \ text { das } ^ 2 $ with a series of numerical experiments, including the parametric lid - driven 2d cavity flow problem with a continuous range of reynolds numbers from 100 to 1000. | arxiv:2402.11283 |
we study a distributed learning problem in which $ n $ agents, each with potentially heterogeneous local data, collaboratively minimize the sum of their local cost functions via peer - to - peer communication. we propose a novel algorithm, spanning tree push - pull ( stpp ), which employs two spanning trees extracted from a general communication graph to distribute both model parameters and stochastic gradients. unlike prior approaches that rely heavily on spectral gap properties, stpp leverages a more flexible topological characterization, enabling robust information flow and efficient updates. theoretically, we prove that stpp achieves linear speedup and polynomial transient iteration complexity, up to $ o ( n ^ 7 ) $ for smooth nonconvex objectives and $ \ tilde { o } ( n ^ 3 ) $ for smooth strongly convex objectives, under arbitrary network topologies. moreover, compared with the existing methods, stpp achieves faster convergence rates on sparse and non - regular topologies ( e. g., directed ring ) and reduces communication overhead on dense networks ( e. g., static exponential graph ). these results significantly advance the state of the art, especially when $ n $ is large. numerical experiments further demonstrate the strong performance of stpp and confirm the practical relevance of its theoretical convergence rates across various common graph architectures. our code is available at https : / / anonymous. 4open. science / r / spanningtreepushpull - 5d3e. | arxiv:2503.16123 |
optical flow estimation is a well - studied topic for automated driving applications. many outstanding optical flow estimation methods have been proposed, but they become erroneous when tested in challenging scenarios that are commonly encountered. despite the increasing use of fisheye cameras for near - field sensing in automated driving, there is very limited literature on optical flow estimation with strong lens distortion. thus we propose and evaluate training strategies to improve a learning - based optical flow algorithm by leveraging the only existing fisheye dataset with optical flow ground truth. while trained with synthetic data, the model demonstrates strong capabilities to generalize to real world fisheye data. the other challenge neglected by existing state - of - the - art algorithms is low light. we propose a novel, generic semi - supervised framework that significantly boosts performances of existing methods in such conditions. to the best of our knowledge, this is the first approach that explicitly handles optical flow estimation in low light. | arxiv:2301.04422 |
kinematic parameter ( kp ) estimation from early electroencephalogram ( eeg ) signals is essential for positive augmentation using wearable robot. however, work related to early estimation of kps from surface eeg is sparse. in this work, a deep learning - based model, bicurnet, is presented for early estimation of biceps curl using collected eeg signal. the model utilizes light - weight architecture with depth - wise separable convolution layers and customized attention module. the feasibility of early estimation of kps is demonstrated using brain source imaging. computationally efficient eeg features in spherical and head harmonics domain is utilized for the first time for kp prediction. the best pearson correlation coefficient ( pcc ) between estimated and actual trajectory of $ 0. 7 $ is achieved when combined eeg features ( spatial and harmonics domain ) in delta band is utilized. robustness of the proposed network is demonstrated for subject - dependent and subject - independent training, using eeg signals with artifacts. | arxiv:2301.03965 |
the twin higgs model seeks to address the little hierarchy problem by making the higgs a pseudo - goldstone of a global $ su ( 4 ) $ symmetry that is spontaneously broken to $ su ( 3 ) $. gauge and yukawa couplings, which explicitly break $ su ( 4 ) $, enjoy a discrete $ \ mathbb { z } _ 2 $ symmetry that accidentally maintains $ su ( 4 ) $ at the quadratic level and therefore keeps the higgs light. contrary to most beyond the standard model theories, the quadratically divergent corrections to the higgs mass are cancelled by a mirror sector, which is uncharged under the standard model groups. however, the twin higgs with an exact $ \ mathbb { z } _ 2 $ symmetry leads to equal vevs in the standard model and mirror sectors, which is phenomenologically unviable. an explicit $ \ mathbb { z } _ 2 $ breaking potential must then be introduced and tuned against the $ su ( 4 ) $ breaking terms to produce a hierarchy of vevs between the two sectors. this leads to a moderate but non - negligible tuning. we propose a model to alleviate this tuning, without the need for an explicit $ \ mathbb { z } _ 2 $ breaking sector. the model consists of two $ su ( 4 ) $ fundamental higgses, one whose vacuum preserves $ \ mathbb { z } _ 2 $ and one whose vacuum breaks it. as the interactions between the two higgses are turned on, the $ \ mathbb { z } _ 2 $ breaking is transmitted from the broken to the unbroken sector and a small hierarchy of vevs is naturally produced. the presence of an effective tadpole and feedback between the two higgses lead to a sizable improvement of the tuning. the resulting higgs boson is naturally very standard model like. | arxiv:1510.06069 |
we present an extension of the allen - cahn / cahn - hilliard system which incorporates a geometrically linear ansatz for the elastic energy of the precipitates. the model contains both the elastic allen - cahn system and the elastic cahn - hilliard system as special cases and accounts for the microstructures on the microscopic scale. we prove the existence of weak solutions to the new model for a general class of energy functionals. we then give several examples of functionals that belong to this class. this includes the energy of geometrically linear elastic materials for d < 3. moreover we show this for d = 3 in the setting of scalar - valued deformations, which corresponds to the case of anti - plane shear. all this is based on explicit formulas for relaxed energy functionals newly derived in this article for d = 1 and d = 3. in these cases we can also prove uniqueness of the weak solutions. | arxiv:1202.5197 |
recent studies have highlighted the presence of cultural biases in large language models ( llms ), yet often lack a robust methodology to dissect these phenomena comprehensively. our work aims to bridge this gap by delving into the food domain, a universally relevant yet culturally diverse aspect of human life. we introduce fmlama, a multilingual dataset centered on food - related cultural facts and variations in food practices. we analyze llms across various architectures and configurations, evaluating their performance in both monolingual and multilingual settings. by leveraging templates in six different languages, we investigate how llms interact with language - specific and cultural knowledge. our findings reveal that ( 1 ) llms demonstrate a pronounced bias towards food knowledge prevalent in the united states ; ( 2 ) incorporating relevant cultural context significantly improves llms ' ability to access cultural knowledge ; ( 3 ) the efficacy of llms in capturing cultural nuances is highly dependent on the interplay between the probing language, the specific model architecture, and the cultural context in question. this research underscores the complexity of integrating cultural understanding into llms and emphasizes the importance of culturally diverse datasets to mitigate biases and enhance model performance across different cultural domains. | arxiv:2404.06833 |
within the standard effective field theory of general relativity, we show that the speed of gravitational waves deviates, ever so slightly, from luminality on cosmological and other spontaneously lorentz - breaking backgrounds. this effect results from loop contributions from massive fields of any spin, including standard model fields, or from tree level effects from massive higher spins $ s \ ge 2 $. we show that for the choice of interaction signs implied by s - matrix and spectral density positivity bounds suggested by analyticity and causality, the speed of gravitational waves is in general superluminal at low - energies on nec preserving backgrounds, meaning gravitational waves travel faster than allowed by the metric to which photons and standard model fields are minimally coupled. we show that departure of the speed from unity increases in the ir and argue that the speed inevitably returns to luminal at high energies as required by lorentz invariance. performing a special tuning of the eft so that renormalization sensitive curvature - squared terms are set to zero, we find that finite loop corrections from standard model fields still lead to an epoch dependent modification of the speed of gravitational waves which is determined by the precise field content of the lightest particles with masses larger than the hubble parameter today. depending on interpretation, such considerations could potentially have far - reaching implications on light scalar models, such as axionic or fuzzy cold dark matter. | arxiv:1909.00881 |
let $ \ sigma _ { g, n } $ be a compact oriented surface with genus $ g \ geq 2 $ bordered by $ n $ circles. due to witten, the twisted reidemeister torsion coincides with a power of the atiyah - bott - goldman - narasimhan symplectic form on the space of representations of $ \ pi _ 1 ( \ sigma _ { g, 0 } ) $ in any semi - simple lie group. in the present paper, we first obtain a multiplicative gluing formula for the twisted reidemeister torsion of $ \ sigma _ { g, 0 } $ in terms of torsions of $ \ sigma _ { 2, 2 }, $ $ \ sigma _ { 2, 1 }, $ and boundary circles $ \ mathbb { s } ^ 1. $ then, by using heusener and porti ' s results on $ \ sigma _ { g, n }, $ we show that the symplectic volume form on the representation variety of $ \ sigma _ { g, 0 } $ can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces $ \ sigma _ { 2, 1 } $ and $ \ sigma _ { 2, 2 }. $ | arxiv:2202.11155 |
we recently introduced a class of $ { \ mathbb { z } } _ n $ graded discrete lax pairs and studied the associated discrete integrable systems ( lattice equations ). in this paper we introduce the corresponding yang - baxter maps. many well known examples belong to this scheme for $ n = 2 $, so, for $ n \ geq 3 $, our systems may be regarded as generalisations of these. in particular, for each $ n $ we introduce a generalisation of the map $ h _ { iii } ^ b $ in the classification of scalar yang - baxter maps. for $ n = 3 $ this is equivalent to the yang - baxter map associated with the discrete modified boussinesq equation. for $ n \ geq 5 $ ( and odd ) we introduce a new family of yang - baxter maps, which have no lower dimensional analogue. we also present multi - component versions of the yang - baxter maps $ f _ { iv } $ and $ f _ v $ ( given in the abs classification ). | arxiv:1510.05590 |
we study a coupled system of navier - stokes equation and the equation of conservation of mass in a one - dimensional network. the system models the blood circulation in arterial networks. a special feature of the system is that the equations are coupled through boundary conditions at joints of the network. we prove the existence and uniqueness of the solution to the initial - boundary value problem, discuss the continuity of dependence of the solution and its derivatives on initial, boundary and forcing functions and their derivatives, develop a numerical scheme that generates discretized solutions, and prove the convergence of the scheme. | arxiv:math-ph/0209015 |
this work is concerned with the detection of a mixture distribution from a $ \ mathbb { r } $ - valued sample. given a sample $ x _ 1, \ dots, x _ n $ and an even density $ \ phi $, our aim is to detect whether the sample distribution is $ \ phi ( \ cdot - \ mu ) $ for some unknown mean $ \ mu $, or is defined as a two - component mixture based on translations of $ \ phi $. we propose a procedure which is based on several spacings of the order statistics, which provides a level - $ \ alpha $ test for all $ n $. our test is therefore a multiple testing procedure and we prove from a theoretical and practical point of view that it automatically adapts to the proportion of the mixture and to the difference of the means of the two components of the mixture under the alternative. from a theoretical point of view, we prove the optimality of the power of our procedure in various situations. a simulation study shows the good performances of our test compared with several classical procedures. | arxiv:1304.6924 |
a theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. a first corollary of that result is that incremental stability may be verified by separation of scaled relative graphs, correcting two assumptions in [ 1, theorem 2 ]. a second corollary provides an incremental version of the classical iqc stability theorem. | arxiv:2412.01580 |
we make two contributions in the field of ai fairness over continuous protected attributes. first, we show that the hirschfeld - gebelein - renyi ( hgr ) indicator ( the only one currently available for such a case ) is valuable but subject to a few crucial limitations regarding semantics, interpretability, and robustness. second, we introduce a family of indicators that are : 1 ) complementary to hgr in terms of semantics ; 2 ) fully interpretable and transparent ; 3 ) robust over finite samples ; 4 ) configurable to suit specific applications. our approach also allows us to define fine - grained constraints to permit certain types of dependence and forbid others selectively. by expanding the available options for continuous protected attributes, our approach represents a significant contribution to the area of fair artificial intelligence. | arxiv:2305.18504 |
in contrast to the static operations of conventional semiconductor devices, the dynamic conformational freedom in molecular devices opens up the possibility of using molecules as new types of devices such as a molecular conformational switch or for molecular data storage. bistable molecules, with e. g. two stable cis and trans isomeric configurations, could provide, once clamped between two electrodes, a switching phenomenon in the nonequilibrium current response. here, we model molecular switch junctions formed at silicon contacts and demonstrate the potential of tunable molecular switches in electrode / molecule / electrode configurations. using the non equilibrium green function approach implemented with the density - functional - based tight - binding theory, a series of properties such as electron transmissions, i - v characteristics in the different isomer - conformations, and potential energy surfaces as a function of the reaction coordinates along the trans to cis transition were calculated. furthermore, in order to investigate stability of molecular switches in ambient conditions, molecular dynamics ( md ) simulations at room temperature were performed and time - dependent fluctuations of the conductance along the md pathways were calculated. our numerical results show that the transmission spectra of the cis isomers are more conductive than trans counterparts inside the bias window for all two model molecules. the current - voltage characteristics consequently show the same trends. additionally, the calculations of time - dependent transmission fluctuations along the md pathways have shown that the transmission in cis isomers is always significantly larger than that of trans counterparts showing that molecular switches can be expected to work as robust molecular switching components. | arxiv:0907.0155 |
we describe various equivalent ways of associating to an orbifold, or more generally a higher \ ' etale differentiable stack, a weak homotopy type. some of these ways extend to arbitrary higher stacks on the site of smooth manifolds, and we show that for a differentiable stack x arising from a lie groupoid g, the weak homotopy type of x agrees with that of bg. using this machinery, we are able to find new presentations for the weak homotopy type of certain classifying spaces. in particular, we give a new presentation for the borel construction of an almost free action of a lie group g on a smooth manifold m as the classifying space of a category whose objects consists of smooth maps r ^ n to m which are transverse to all the g - orbits, where n = dim m - dim g. we also prove a generalization of segal ' s theorem, which presents the weak homotopy type of haefliger ' s groupoid $ \ gamma ^ q $ as the classifying space of the monoid of self - embeddings of r ^ q, and our generalization gives analogous presentations for the weak homotopy type of the lie groupoids $ \ gamma ^ { sp } _ { 2q } $ and $ r \ gamma ^ q $ which are related to the classification of foliations with transverse symplectic forms and transverse metrics respectively. we also give a short and simple proof of segal ' s original theorem using our machinery. | arxiv:1504.02394 |
moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. particular examples of abstract moment maps had been used in hamiltonian mechanics for some time, but the abstract notion originated in the study of cobordisms of hamiltonian group actions. in this paper we answer the question of existence of a ( proper ) abstract moment map for a torus action and give a necessary and sufficient condition for an abstract moment map to be associated with a pre - symplectic form. this is done by using the notion of an assignment, which is a combinatorial counterpart of an abstract moment map. finally, we show that the space of assignments fits as the zeroth cohomology in a series of certain cohomology spaces associated with a torus action on a manifold. we study the resulting " assignment cohomology " theory. | arxiv:math/9904117 |
we argue that the changing - look event in the active galactic nucleus 1es 1927 + 654, followed by a dip of 3 orders of magnitude in the x - ray luminosity, is controlled by a change in the accretion rate and an inversion of magnetic flux in a magnetically arrested disk ( mad ). before the changing - look event, strong magnetic flux on the black hole powers x - ray emission via the blandford - znajek process while the uv emission is produced by a radiatively inefficient magnetized disk. an advection event, bringing flux of the opposite polarity, propagates inward leading, first, to a rise in the uv / optical luminosity and, then, to a dip in the x - ray luminosity when it reaches the black hole. we estimate the timescale for magnetic flux advection and find that the observed timescale between the beginning of the changing - look event and the minimum in the x - ray luminosity, $ \ approx200 $ days, is in agreement with the time needed to cancel the magnetic flux in a mad extending to $ \ approx180 \ : r _ g $. although flux inversion events might be rare due to the large ratio of flux - to - mass that is needed, we argue that agn showing an unusually high ratio of x - ray to uv luminosity are prime candidates for such events. we also suggest that similar events may lead to jet interruptions in radio - loud objects. | arxiv:2011.01954 |
the unpolarised differential cross section and the two deuteron tensor analysing powers a _ { xx } and a _ { yy } of the pol { d } p - > ( pp ) n charge - exchange reaction have been measured with the anke spectrometer at the cosy storage ring. using deuteron beams with energies 1. 2, 1. 6, 1. 8, and 2. 27 gev, data were obtained for small momentum transfers to a ( pp ) system with low excitation energy. the results at the three lower energies are consistent with impulse approximation predictions based upon the current knowledge of the neutron - proton amplitudes. however, at 2. 27gev, where these amplitudes are far more uncertain, agreement requires a reduction in the overall double - spin - flip contribution, with an especially significant effect in the longitudinal direction. these conclusions are supported by measurements of the deuteron - proton spin - correlation parameters c _ { x, x } and c _ { y, y } that were carried out in the pol { d } pol { p } - > ( pp ) n reaction at 1. 2 and 2. 27gev. the values obtained for the proton analysing power also suggest the need for a radical re - evaluation of the neutron - proton elastic scattering amplitudes at the higher energy. it is therefore clear that such measurements can provide a valuable addition to the neutron - proton database in the charge - exchange region. | arxiv:1212.2365 |
accurate segmentation of glomerulus instances attains high clinical significance in the automated analysis of renal biopsies to aid in diagnosing and monitoring kidney disease. analyzing real - world histopathology images often encompasses inter - observer variability and requires a labor - intensive process of data annotation. therefore, conventional supervised learning approaches generally achieve sub - optimal performance when applied to external datasets. considering these challenges, we present a semi - supervised learning approach for glomeruli segmentation based on the weak - to - strong consistency framework validated on multiple real - world datasets. our experimental results on 3 independent datasets indicate superior performance of our approach as compared with existing supervised baseline models such as u - net and segformer. | arxiv:2406.16900 |
the stationary radial distribution, $ p ( \ rho ) $, of the random walk with the diffusion coefficient $ d $, which winds with the tangential velocity $ v $ around the impenetrable disc of radius $ r $ for $ r \ gg 1 $ converges to the distribution involving the airy function. typical trajectories are localized in the circular strip $ [ r, r + \ delta r ^ { 1 / 3 } ] $, where $ \ delta $ is the constant which depends on the parameters $ d $ and $ v $ and is independent on $ r $. | arxiv:2002.09965 |
we extend the the combinatorics of tableaux to the study of diagram algebras and give a uniform construction of their quasi - hereditary covers. | arxiv:1102.0743 |
we present a quantum secure direct communication ( qsdc ) scheme as an extension for a proposed supervised secure entanglement sharing protocol. starting with a quick review on the supervised entanglement sharing protocol - - the " wuhan " protocol [ y. li and y. liu, arxiv : 0709. 1449v2 ], we primarily focus on its further extend using for a qsdc task, in which the communication attendant alice encodes the secret message directly onto a sequence of 2 - level particles which then can be faithfully teleported to bob using the shared maximal entanglement states obtained by the previous " wuhan " protocol. we also evaluate the security of the qsdc scheme, where an individual self - attack performed by alice and bob - - the out of control attack ( oca ) is introduced and the robustness of our scheme on the oca is documented. | arxiv:0711.2827 |
a light - weight low - resolution face gender classification method, called facehop, is proposed in this research. we have witnessed rapid progress in face gender classification accuracy due to the adoption of deep learning ( dl ) technology. yet, dl - based systems are not suitable for resource - constrained environments with limited networking and computing. facehop offers an interpretable non - parametric machine learning solution. it has desired characteristics such as a small model size, a small training data amount, low training complexity, and low - resolution input images. facehop is developed with the successive subspace learning ( ssl ) principle and built upon the foundation of pixelhop + +. the effectiveness of the facehop method is demonstrated by experiments. for gray - scale face images of resolution $ 32 \ times 32 $ in the lfw and the cmu multi - pie datasets, facehop achieves correct gender classification rates of 94. 63 % and 95. 12 % with model sizes of 16. 9k and 17. 6k parameters, respectively. it outperforms lenet - 5 in classification accuracy while lenet - 5 has a model size of 75. 8k parameters. | arxiv:2007.09510 |
gamma ray bursts ( grbs ) show evidence of different spectral shapes, light curves, duration, host galaxies and they explode within a wide redshift range. however, the most of them seems to follow very tight correlations among some observed quantities relating to their energetic. if true, these correlations have significant implications on burst physics, giving constraints on theoretical models. moreover, several suggestions have been made to use these correlations in order to calibrate grbs as standard candles and to constrain the cosmological parameters. we investigate the cosmological relation between low energy $ \ alpha $ index in grbs prompt spectra and the redshift $ z $. we present a statistical analysis of the relation between the total isotropic energy $ e _ { iso } $ and the peak energy $ e _ p $ ( also known as amati relation ) in grbs spectra searching for possible functional biases. possible implications on the $ e _ { iso } $ vs $ e _ p $ relation of the $ \ alpha $ vs $ ( 1 + z ) $ correlation are evaluated. we used montecarlo simulations and the boostrap method to evaluate how large are the effects of functional biases on the $ e _ { iso } $ vs $ e _ p $. we show that high values of the linear correlation coefficent, up to about 0. 8, in the $ e _ { iso } $ vs $ e _ p $ relation are obtained for random generated samples of grbs, confirming the relevance of functional biases. astrophysical consequences from $ e _ { iso } $ vs $ e _ p $ relation are then to be revised after a more accurate and possibly bias free analysis. | arxiv:0710.2226 |
the influence of a neutrinoless electron to positron conversion on a cooling of strongly magnetized iron white dwarfs is studied. | arxiv:1312.5343 |
in a recent paper [ 1 ], three - particle interactions without invariance under lorentz boosts were constrained by demanding that they yield tree - level four - particle scattering amplitudes with singularities as dictated by unitarity and locality. in this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using bcfw momentum shifts. we point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite bcfw parameter z, is not strictly necessary to obtain non - trivial constraints for the three - particle interactions. | arxiv:2009.14289 |
a path p ( k, l, r ) is an oriented path consisting of k forward arcs, followed by l backward arcs, and then by r forward arcs. we prove the existence of any oriented path of length n - 1 with three blocks having the middle block of length one in any ( 2n - 3 ) - chromatic digraph, which is an improvement of the latest bound reached in this case. concerning the general case of paths with three blocks, we prove, after partitioning the problem into three cases according to the value of k, l and r that the chromatic number of digraphs containing no p ( k, l, r ) of length n - 1 is bounded above by 2 ( n - 1 ) + r, 2 ( n - 1 ) + l + r - k and 2 ( n + l - 1 ) - k in the three cases respectively. | arxiv:2312.09905 |
we have fabricated carbon nanotube ( cn ) field - effect transistors with multiple, individually addressable gate segments. the devices exhibit markedly different transistor characteristics when switched using gate segments controlling the device interior versus those near the source and drain. we ascribe this difference to a change from schottky barrier modulation at the contacts to bulk switching. we also find that the current through the bulk portion is independent of gate length for any gate voltage, offering direct evidence for ballistic transport in semiconducting cns over at least a few hundred nanometers, even for relatively small carrier velocities. | arxiv:cond-mat/0306295 |
we consider a discrete and a continuum model for the propagation of a curvature sensitive interface in a time independent random medium. in both cases we suppose that the medium contains obstacles that act on the propagation of the interface with an inhibitory or an acceleratory force. we show that the interface remains bounded for all times even when a small constant external driving force is applied. this phenomenon has already been known when only inhibitory obstacles are present. in this work we extend this result to the case of, for example, a random medium of random zero mean forcing. | arxiv:2002.00800 |
we investigate the single - photon transport in a single - mode optical fiber coupled to an optomechanical system in the single - photon strong - coupling regime. the single - photon transmission amplitude is analytically obtained with a real - space approach and the effects of thermal noises are studied via master - equation simulations. the results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. based on the theoretical framework, we further propose a scheme to generate the mechanical noon states with arbitrary phonon numbers by measuring the sideband photons. the probability for generating the noon state with five phonons is over 0. 15. | arxiv:1210.4275 |
the composition and site occupancy of mg within ordered { \ delta } precipitates in a model al mg li alloy have been characterized by atom probe microscopy and first - principles simulations. the concentration in the precipitates is found to be almost the same as that of the matrix, however, we show evidence that mg partitions to the sites normally occupied by li in the l12 structure. density functional calculations demonstrate that this partition is energetically favorable, in agreement with experimental results. | arxiv:1510.02910 |
let $ \ overline { m } $ be a compact complex manifold with smooth k \ " ahler metric $ \ eta $, and let $ d $ be a smooth divisor on $ \ overline { m } $. let $ m = \ overline { m } \ setminus d $ and let $ \ hat { \ omega } $ be a carlson - griffiths type metric on $ m $. we study complete solutions to k \ " ahler - ricci flow on $ m $ which are comparable to $ \ hat { \ omega } $, starting from a smooth initial metric $ \ omega _ 0 = \ eta + i \ partial \ bar { \ partial } \ phi _ 0 $ where $ \ phi _ 0 \ in c ^ { \ infty } ( m ) $. when $ \ omega _ 0 \ geq c \ hat { \ omega } $ on $ m $ for some $ c > 0 $ and $ \ phi _ 0 $ has zero lelong number, we construct a smooth solution $ \ omega ( t ) $ to k \ " ahler - ricci flow on $ m \ times [ 0, t _ { [ \ omega _ 0 ] } ) $ where $ t _ { [ \ omega _ 0 ] } : = \ sup \ { t : [ \ eta ] + t ( c _ 1 ( k _ { \ overline { m } } ) + c _ 1 ( \ mathcal { o } _ d ) ) \ in \ mathcal { k } _ m \ } $ so that $ \ omega ( t ) \ geq ( \ frac { 1 } { n } - \ frac { 4 \ hat { k } t } { c } ) \ hat { \ omega } $ for all $ t \ leq \ frac { c } { 4n \ hat { k } } $ where $ \ hat { k } $ is a non - negative upper bound on the bisectional curvatures of $ \ hat { \ omega } $ ( see theorem 1. 2 ). in particular, we do not assume $ \ omega _ 0 $ has bounded curvature. if $ \ omega _ 0 $ has bounded curvature and is asymptotic to $ \ hat { \ omega } $ in an appropriate sense, we construct a complete bounded curvature solution on $ m \ times [ 0, t _ { [ \ omega _ 0 ] } ) $ ( see theorem 1. 3 ). these general | arxiv:1708.02717 |
we study continuous time markov processes on graphs. the notion of frequency is introduced, which serves well as a scaling factor between any markov time of a continuous time markov process and that of its jump chain. as an application, we study ` ` multi - person simple random walks ' ' on a graph g with n vertices. there are n persons distributed randomly at the vertices of g. in each step of this discrete time markov process, we randomly pick up a person and move it to a random adjacent vertex. we give estimate on the expected number of steps for these $ n $ persons to meet all together at a specific vertex, given that they are at different vertices at the begininng. for regular graphs, our estimate is exact. | arxiv:math/0410298 |
the phase stability of the ( bi2 ) m ( bi2te3 ) n natural superlattices has been investigated through the low temperature solid state synthesis of a number of new binary bixte1 - x compositions. powder x - ray diffraction revealed that an infinitely adaptive series forms for 0. 44 < x < 0. 70, while an unusual 2 - phase region with continuously changing compositions is observed for 0. 41 < x < 0. 43. for x > 0. 70, mixtures of elemental bi and an almost constant composition ( bi2 ) m ( bi2te3 ) n phase are observed. rietveld analysis of synchrotron x - ray powder diffraction data collected on bi2te ( m = 2, n = 1 ) revealed substantial interchange of bi and te between the bi2 and bi2te3 blocks, demonstrating that the block compositions are variable. all investigated phase pure compositions are degenerate semiconductors with low residual resistivity ratios and moderate positive magnetoresistances ( r / r0 = 1. 05 in 9 t ). the maximum seebeck coefficient is + 80 muv k - 1 for x = 0. 63, leading to an estimated thermoelectric figure of merit, zt = 0. 2 at 250 k. | arxiv:1204.0356 |
to deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. here we present stability constraints for the one - dimensional counterpart of this morphoelastic model, for both the continuous and ( semi - ) discrete problem. we show that the truncation error between these eigenvalues associated with the continuous and semi - discrete problem is of order $ \ mathcal { o } ( h ^ 2 ) $. next, we perform numerical validation to these constraints and provide a biological interpretation of the ( in ) stability. for the mechanical part of the model, the results show the components reach equilibria in a ( non ) monotonic way, depending on the value of the viscosity. the results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results. | arxiv:2010.12897 |
we derive the minimum observing time scales to detect a blazar at a given flux level with the lat on glast in the scanning and pointing modes. based upon phase 1 observations with egret, we predict the glast detection rate of blazar flares at different flux levels. with some uncertainty given the poor statistics of bright blazars, we predict that a blazar flare with integral flux > ~ 200e - 8 ph ( > 100 mev ) cm ^ { - 2 } s ^ { - 1 }, which are the best candidates for target of opportunity pointings and extensive temporal and spectral studies, should occur every few days. | arxiv:astro-ph/0312590 |
this paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. we propose a novel multiway empirical likelihood statistic that converges to a chi - square distribution under the non - degenerate case, where corresponding hoeffding type decomposition is dominated by linear terms. our methodology is related to the notion of jackknife empirical likelihood but the leave - out pseudo values are constructed by leaving columns or rows. we further develop a modified version of our multiway empirical likelihood statistic, which converges to a chi - square distribution regardless of the degeneracy, and discover its desirable higher - order property compared to the t - ratio by the conventional eicker - white type variance estimator. the proposed methodology is illustrated by several important statistical problems, such as bipartite network, generalized estimating equations, and three - way observations. | arxiv:2108.04852 |
we present a framework for learning node embeddings from static subgraphs ( ness ) using a graph autoencoder ( gae ) in a transductive setting. ness is based on two key ideas : i ) partitioning the training graph to multiple static, sparse subgraphs with non - overlapping edges using random edge split during data pre - processing, ii ) aggregating the node representations learned from each subgraph to obtain a joint representation of the graph at test time. moreover, we propose an optional contrastive learning approach in transductive setting. we demonstrate that ness gives a better node representation for link prediction tasks compared to current autoencoding methods that use either the whole graph or stochastic subgraphs. our experiments also show that ness improves the performance of a wide range of graph encoders and achieves state - of - the - art results for link prediction on multiple real - world datasets with edge homophily ratio ranging from strong heterophily to strong homophily. | arxiv:2303.08958 |
we present a comprehensive x - ray study of four years of pointed rxte observations of grs 1915 + 105 in the chi - state. we interpret the behavior of the hard power law tail spectrum as coming from inverse compton scattering of soft disk photons on a thermally dominated hybrid corona above the accretion disk. grs 1915 + 105 shows a strong, variable reflection amplitude. as in other bhc and in seyfert galaxies, a correlation between the power law slope and the reflection was found. also, the radio fluxes at 2. 25 ghz and 15 ghz correlate with the power law slope, thus revealing a connection between the outflowing matter and the comptonizing region in the chi - states. | arxiv:astro-ph/0207474 |
gravitational waves from binary neutron stars in quasiequilibrium circular orbits are computed using an approximate method which we propose in this paper. in the first step of this method, we prepare general relativistic irrotational binary neutron stars in a quasiequilibrium circular orbit, neglecting gravitational waves. we adopt the so - called conformal flatness approximation for a three - metric to obtain the quasiequilibrium states in this paper. in the second step, we compute gravitational waves, solving linear perturbation equations in the background spacetime of the quasiequilibrium states. comparing numerical results with post newtonian waveforms and luminosity of gravitational waves from two point masses in circular orbits, we demonstrate that this method can produce accurate waveforms and luminosity of gravitational waves. it is shown that the effects of tidal deformation of neutron stars and strong general relativistic gravity modify the post newtonian results for compact binary neutron stars in close orbits. we indicate that the magnitude of a systematic error in quasiequilibrium states associated with the conformal flatness approximation is fairly large for close and compact binary neutron stars. several formulations for improving the accuracy of quasiequilibrium states are proposed. | arxiv:gr-qc/0109026 |
we have realized a dual - species bose - einstein condensate ( bec ) of $ ^ { 23 } $ na and $ ^ { 87 } $ rb atoms and observed their immiscibility. because of the favorable background intra - and inter - species scattering lengths, stable condensates can be obtained via efficient evaporative cooling and sympathetic cooling without the need for fine tuning of the interactions. our system thus provides a clean platform for studying inter - species interactions driven effects in superfluid mixtures. with a feshbach resonance, we have successfully created double becs with largely tunable inter - species interactions and studied the miscible - immiscible phase transition. | arxiv:1305.7091 |
in 1979, gonek presented the hybrid joint universality theorem for dirichlet $ l $ - functions and proved the universality theorem for hurwitz zeta - functions with rational parameter as an application. following the introduction of the hybrid universality theorem, several generalizations, refinements, and applications have been developed. despite these advancements, no probabilistic proof based on bagchi ' s approach has been formulated due to the complexities of adapting his method to the hybrid joint universality theorem. in this paper, we prove the limit theorem for the hybrid joint universality theorem. | arxiv:2410.17575 |
datacenters act as cloud - infrastructure to stakeholders across industry, government, and academia. to meet growing demand yet operate efficiently, datacenter operators employ increasingly more sophisticated scheduling systems, mechanisms, and policies. although many scheduling techniques already exist, relatively little research has gone into the abstraction of the scheduling process itself, hampering design, tuning, and comparison of existing techniques. in this work, we propose a reference architecture for datacenter schedulers. the architecture follows five design principles : components with clearly distinct responsibilities, grouping of related components where possible, separation of mechanism from policy, scheduling as complex workflow, and hierarchical multi - scheduler structure. to demonstrate the validity of the reference architecture, we map to it state - of - the - art datacenter schedulers. we find scheduler - stages are commonly underspecified in peer - reviewed publications. through trace - based simulation and real - world experiments, we show underspecification of scheduler - stages can lead to significant variations in performance. | arxiv:1808.04224 |
we experimentally demonstrate a method to determine the temperature of trapped ions which is suitable for monitoring fast thermalization processes. we show that observing and analyzing the lineshape of dark resonances in the fluorescence spectrum provides a temperature measurement which accurate over a large dynamic range, applied to single ions and small ion crystals. laser induced fluorescence is detected over a time of only $ 20 \, \ mu $ s allowing for rapid determination of the ion temperature. in the measurement range of $ 10 ^ { - 1 } - 10 ^ { + 2 } \, $ mk we reach better than $ 15 \, \ % $ accuracy. tuning the cooling laser to selected resonance features allows for controlling the ion temperatures between $ 0. 7 \, $ mk and more than $ 10 \, $ mk. experimental work is supported by a solution of the 8 - level optical bloch equations when including the ions classical motion. this technique paves the way for many experiments comprising heat transport in ion strings, heat engines, non - equilibrium thermodynamics or thermometry of large ion crystals. | arxiv:1412.5014 |
for pulsar projects it is often necessary to predict the pulse phase in advance, for example, when preparing for new observations. interpolation of the pulse phase between existing measurements is also often required, for example, when folding x - ray or gamma - ray observations according to the radio pulse phase. until now these procedures have been done using various ad hoc methods. the purpose of this paper is to show how to interpolate or predict the pulse phase optimally using statistical models of the various noise processes and the phase measurement uncertainty. | arxiv:1204.6111 |
we present iron and $ \ alpha $ element ( mg, ca, ti ) abundances for a sample of 15 red giant branch stars belonging to the main body of the sagittarius dwarf spheroidal galaxy. abundances have been obtained from spectra collected using the high resolution spectrograph flames - uves mounted at the vlt. stars of our sample have a mean metallicity of [ fe / h ] = - 0. 41 $ \ pm $ 0. 20 with a metal poor tail extending to [ fe / h ] = - 1. 52. the $ \ alpha $ element abundance ratios are slightly subsolar for metallicities higher than [ fe / h ] \ gtsima - 1, suggesting a slow star formation rate. the [ $ \ alpha $ / fe ] of stars having [ fe / h ] $ < $ - 1 are compatible to what observed in milky way stars of comparable metallicity. | arxiv:astro-ph/0506622 |
driven by b5g and 6g technologies, multi - network fusion is an indispensable tendency for future communications. in this paper, we focus on and analyze the \ emph { security performance } ( sp ) of the \ emph { satellite - terrestrial downlink transmission } ( stdt ). here, the stdt is composed of a satellite network and a vehicular network with a legitimate mobile receiver and an mobile eavesdropper distributing. to theoretically analyze the sp of this system from the perspective of mobile terminals better, the random geometry theory is adopted, which assumes that both terrestrial vehicles are distributed stochastically in one beam of the satellite. furthermore, based on this theory, the closed - form analytical expressions for two crucial and specific indicators in the stdt are derived, respectively, the secrecy outage probability and the ergodic secrecy capacity. additionally, several related variables restricting the sp of the stdt are discussed, and specific schemes are presented to enhance the sp. then, the asymptotic property is investigated in the high signal - to - noise ratio scenario, and accurate and asymptotic closed - form expressions are given. finally, simulation results show that, under the precondition of guaranteeing the reliability of the stdt, the asymptotic solutions outperform the corresponding accurate results significantly in the effectiveness. | arxiv:2112.14192 |
an eigenvalue of the adjacency matrix of a graph is said to be main if the all - ones vector is not orthogonal to its associated eigenspace. a generalized bethe tree with $ k $ levels is a rooted tree in which vertices at the same level have the same degree. fran \ c { c } a and brondani [ on the main spectrum of generalized bethe trees, linear algebra appl., 628 ( 2021 ) 56 - 71 ] recently conjectured that any generalized bethe tree with $ k $ levels has exactly $ k $ main eigenvalues whenever $ k $ is even. we disprove the conjecture by constructing a family of counterexamples for even integers $ k \ ge 6 $. | arxiv:2201.01101 |
in nielsen ' s geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the group manifold. earlier work has shown that the computation of geodesic distance can be challenging for lie groups relevant to harmonic oscillators. here, this problem is approached by working to leading order in an expansion by the structure constants of the lie group. an explicit formula for an upper bound on the quantum complexity of a harmonic oscillator hamiltonian with time - dependent frequency is derived. applied to a massless test scalar field on a cosmological de sitter background, the upper bound on complexity as a function of the scale factor exhibits a logarithmic increase on super - hubble scales. this result aligns with the gate complexity and earlier studies of de sitter complexity. it demonstrates the consistent application of nielsen complexity to quantum fields in cosmological backgrounds and paves the way for further applications. | arxiv:2407.01677 |
we theoretically investigate disorder effects on the ferromagnetic transition ( ' curie ' ) temperature $ t _ c $ in dilute iii $ _ { 1 - x } $ mn $ _ x $ v magnetic semiconductors ( e. g. ga $ _ { 1 - x } $ mn $ _ x $ as ) where a small fraction ( $ x \ approx 0. 01 - 0. 1 $ ) of the cation atoms ( e. g. ga ) are randomly replaced by the magnetic dopants ( e. g. mn ), leading to long - range ferromagnetic ordering for $ t < t _ c $. we find that $ t _ c $ is a complicated function of at least eight different parameters including carrier density, magnetic dopant density, and carrier mean free path ; nominally macroscopically similar samples could have substantially different curie temperatures. we provide simple physically appealing prescriptions for enhancing $ t _ c $ in diluted magnetic semiconductors, and discuss the magnetic phase diagram in the system parameter space. | arxiv:cond-mat/0403059 |
we recently described a general solution to the phase matching problem that arises when one wishes to perform an arbitrary number of nonlinear optical processes in a single medium [ prl 95 ( 2005 ) 133901 ]. here we outline in detail the implementation of the solution for a one dimensional photonic quasicrystal which acts as a simultaneous frequency doubler for three independent optical beams. we confirm this solution experimentally using an electric field poled ktiopo $ _ 4 $ crystal. in optimizing the device, we find - contrary to common practice - that simple duty cycles of 100 % and 0 % may yield the highest efficiencies, and show that our device is more efficient than a comparable device based on periodic quasi - phase - matching. | arxiv:cond-mat/0701358 |
duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. ( hodge - dirac - ) dualisation of gauge potentials exchanges noether and topological charges, equations of motion and bianchi identities, internal rigid symmetries and gauge symmetries, local transformations with nonlocal ones and most exciting particles and waves. we compare the actions of maximally dualised supergravities ( ie with gauge potential forms of lowest possible degree ) to the non - dualised actions coming from 11 ( or 10 ) dimensions by plain dimensional reduction as well as to other theories with partial dualisations. the effect on the rigid duality group is a kind of contraction resulting from the elimination of the unfaithful generators associated to the ( inversely ) dualised scalar fields. new gauge symmetries are introduced by these ( un ) dualisations and it is clear that a complete picture of duality ( f ( ull ) - duality ) should include all gauge symmetries at the same time as the rigid symmetries and the spacetime symmetries. we may read off some properties of f - duality on the internal rigid dynkin diagram : field content, possible dualisations, increase of the rank according to the decrease of space dimension... some recent results are included to suggest the way towards unification via a universal twisted self - duality ( ts ) structure. the analysis of this structure had revealed several profound differences according to the parity mod 4 of the dimension of spacetime ( to be contrasted with the ( bott ) period 8 of spinor properties ). | arxiv:hep-th/9805083 |
we consider the problem of computing the value adjustment of european contingent claims when default of either party is considered, possibly including also funding and collateralization requirements. as shown in brigo et al. ( \ cite { blps }, \ cite { bfp } ), this leads to a more articulate variety of value adjustments ( { xva } ) that introduce some nonlinear features. when exploiting a reduced - form approach for the default times, the adjusted price can be characterized as the solution to a possibly nonlinear backward stochastic differential equation ( bsde ). the expectation representing the solution of the bsde is usually quite hard to compute even in a markovian setting, and one might resort either to the discretization of the partial differential equation characterizing it or to monte carlo simulations. both choices are computationally very expensive and in this paper we suggest an approximation method based on an appropriate change of numeraire and on a taylor ' s polynomial expansion when intensities are represented by means of affine processes correlated with the asset ' s price. the numerical discussion at the end of this work shows that, at least in the case of the cir intensity model, even the simple first - order approximation has a remarkable computational efficiency. | arxiv:2007.07701 |
in this note we construct bi - * - galois objects linking the quantized universal enveloping algebras associated to the lie groups su ( 2 ), e ( 2 ) and su ( 1, 1 ), where e ( 2 ) denotes the lie group of euclidian transformations of the plane, and we show how one can create ( formal ) quantum homogeneous spaces for these quantum groups by integrating the associated miyashita - ulbrich action on certain subquotient * - algebras. | arxiv:1001.2153 |
we present high spatial resolution $ ^ { 12 } $ co ( $ j = 1 - 0 $ ) images taken by the nobeyama 45m telescope toward a $ 48 ' \ times 48 ' $ area including the l1641 - n cluster. the effective spatial resolution of the maps is $ 21 " $, corresponding to 0. 04 pc at a distance of 400 pc. a recent 1. 1 mm dust continuum map reveals that the dense gas is concentrated in several thin filaments. we find that a few dust filaments are located at the parts where $ ^ { 12 } $ co ( $ j = 1 - 0 $ ) emission drops sharply. furthermore, the filaments have two - components with different velocities. the velocity difference between the two - components is about 3 km s $ ^ { - 1 } $, corresponding to a mach number of 10, significantly larger than the local turbulent velocity in the cloud. these facts imply that the collision of the two components ( hereafter, the cloud - cloud collision ) possibly contributed to the formation of these filaments. since the two components appear to overlap toward the filaments on the plane of the sky, the collision may have occurred almost along the line of sight. star formation in the l1641 - n cluster was probably triggered by such a collision. we also find several parsec - scale co shells whose centers are close to either the l1641 - n cluster or v 380 ori cluster. we propose that these shells were created by multiple winds and / or outflows from cluster ysos, i. e., " protocluster winds. " one exceptional dust filament located at the western cloud edge lies along a shell ; it is presumably a part of the expanding shell. both the cloud - cloud collision and protocluster winds are likely to influence the cloud structure and kinematics in this region. | arxiv:1110.6225 |
we study theoretically the dynamical process of yielding in cyclically sheared amorphous materials, within a thermal elastoplastic model and the soft glassy rheology model. within both models we find an initially slow accumulation, over many cycles after the inception of shear, of low levels of damage in the form strain heterogeneity across the sample. this slow fatigue then suddenly gives way to catastrophic yielding and material failure. strong strain localisation in the form of shear banding is key to the failure mechanism. we characterise in detail the dependence of the number of cycles n * before failure on the amplitude of imposed strain, the working temperature, and the degree to which the sample is annealed prior to shear. we discuss our finding with reference to existing experiments and particle simulations, and suggest new ones to test our predictions. | arxiv:2211.11677 |
we force the existence of a non - trivial $ \ kappa $ - complete ultrafilter over $ \ kappa $ which fails to satisfy the galvin property. this answers a question asked by the first author and moti gitik. | arxiv:2111.11823 |
( a + b ) } and a radius of 1 2 ( b − a ). { \ displaystyle { \ tfrac { 1 } { 2 } } ( b - a ). } the closed finite interval [ a, b ] { \ displaystyle [ a, b ] } is the corresponding closed ball, and the interval ' s two endpoints { a, b } { \ displaystyle \ { a, b \ } } form a 0 - dimensional sphere. generalized to n { \ displaystyle n } - dimensional euclidean space, a ball is the set of points whose distance from the center is less than the radius. in the 2 - dimensional case, a ball is called a disk. if a half - space is taken as a kind of degenerate ball ( without a well - defined center or radius ), a half - space can be taken as analogous to a half - bounded interval, with its boundary plane as the ( degenerate ) sphere corresponding to the finite endpoint. = = = multi - dimensional intervals = = = a finite interval is ( the interior of ) a 1 - dimensional hyperrectangle. generalized to real coordinate space r n, { \ displaystyle \ mathbb { r } ^ { n }, } an axis - aligned hyperrectangle ( or box ) is the cartesian product of n { \ displaystyle n } finite intervals. for n = 2 { \ displaystyle n = 2 } this is a rectangle ; for n = 3 { \ displaystyle n = 3 } this is a rectangular cuboid ( also called a " box " ). allowing for a mix of open, closed, and infinite endpoints, the cartesian product of any n { \ displaystyle n } intervals, i = i 1 × i 2 × × i n { \ displaystyle i = i _ { 1 } \ times i _ { 2 } \ times \ cdots \ times i _ { n } } is sometimes called an n { \ displaystyle n } - dimensional interval. a facet of such an interval i { \ displaystyle i } is the result of replacing any non - degenerate interval factor i k { \ displaystyle i _ { k } } by a degenerate interval consisting of a finite endpoint of i k. { \ displaystyle i _ { k }. } the faces of i { \ displaystyle i } comprise i { \ displaystyle i } itself and all faces of its facets. | https://en.wikipedia.org/wiki/Interval_(mathematics) |
determining the nature of electronic states in doped mott insulators remains a challenging task. in the case of tetragonal la $ _ { 2 - x } $ sr $ _ { x } $ nio $ _ { 4 } $, the occurrence of diagonal charge and spin stripe order in the ground state is now well established. in contrast, the nature of the high - temperature " disordered " state from which the stripe order develops has long been a subject of controversy, with considerable speculation regarding a polaronic liquid. following on the recent detection of dynamic charge stripes, we use neutron scattering measurements on an $ x = 0. 25 $ crystal to demonstrate that the dispersion of the charge stripe excitations is anisotropic. this observation provides compelling evidence for the presence of electronic nematic order. | arxiv:1608.04799 |
for more than a decade, researchers have measured progress in object recognition on imagenet - based generalization benchmarks such as imagenet - a, - c, and - r. recent advances in foundation models, trained on orders of magnitude more data, have begun to saturate these standard benchmarks, but remain brittle in practice. this suggests standard benchmarks, which tend to focus on predefined or synthetic changes, may not be sufficient for measuring real world generalization. consequently, we propose studying generalization across geography as a more realistic measure of progress using two datasets of objects from households across the globe. we conduct an extensive empirical evaluation of progress across nearly 100 vision models up to most recent foundation models. we first identify a progress gap between standard benchmarks and real - world, geographical shifts : progress on imagenet results in up to 2. 5x more progress on standard generalization benchmarks than real - world distribution shifts. second, we study model generalization across geographies by measuring the disparities in performance across regions, a more fine - grained measure of real world generalization. we observe all models have large geographic disparities, even foundation clip models, with differences of 7 - 20 % in accuracy between regions. counter to modern intuition, we discover progress on standard benchmarks fails to improve geographic disparities and often exacerbates them : geographic disparities between the least performant models and today ' s best models have more than tripled. our results suggest scaling alone is insufficient for consistent robustness to real - world distribution shifts. finally, we highlight in early experiments how simple last layer retraining on more representative, curated data can complement scaling as a promising direction of future work, reducing geographic disparity on both benchmarks by over two - thirds. | arxiv:2307.13136 |
a $ ( p, q ) $ - coloring of a graph $ g $ is an edge - coloring of $ g $ which assigns at least $ q $ colors to each $ p $ - clique. the problem of determining the minimum number of colors, $ f ( n, p, q ) $, needed to give a $ ( p, q ) $ - coloring of the complete graph $ k _ n $ is a natural generalization of the well - known problem of identifying the diagonal ramsey numbers $ r _ k ( p ) $. the best - known general upper bound on $ f ( n, p, q ) $ was given by erd \ h { o } s and gy \ ' arf \ ' as in 1997 using a probabilistic argument. since then, improved bounds in the cases where $ p = q $ have been obtained only for $ p \ in \ { 4, 5 \ } $, each of which was proved by giving a deterministic construction which combined a $ ( p, p - 1 ) $ - coloring using few colors with an algebraic coloring. in this paper, we provide a framework for proving new upper bounds on $ f ( n, p, p ) $ in the style of these earlier constructions. we characterize all colorings of $ p $ - cliques with $ p - 1 $ colors which can appear in our modified version of the $ ( p, p - 1 ) $ - coloring of conlon, fox, lee, and sudakov. this allows us to greatly reduce the amount of case - checking required in identifying $ ( p, p ) $ - colorings, which would otherwise make this problem intractable for large values of $ p $. in addition, we generalize our algebraic coloring from the $ p = 5 $ setting and use this to give improved upper bounds on $ f ( n, 6, 6 ) $ and $ f ( n, 8, 8 ) $. | arxiv:2006.09577 |
we develop a maximum likelihood method to infer relevant physical properties of elongated active particles. using individual trajectories of advected swimmers as input, we are able to accurately determine their rotational diffusion coefficients and an effective measure of their aspect ratio, also providing reliable estimators for the uncertainties of such quantities. we validate our theoretical construction using numerically generated active trajectories upon no - flow, simple shear, and poiseuille flow, with excellent results. being designed to rely on single - particle data, our method eases applications in experimental conditions where swimmers exhibit a strong morphological diversity. we briefly discuss some of such ongoing experimental applications, specifically, in the characterization of swimming e. coli in a flow. | arxiv:2012.04528 |
let $ \ mathcal { x } $ be a regular projective arithmetic variety equipped with an ample hermitian line bundle $ \ overline { \ mathcal { l } } $. we prove that the proportion of global sections $ \ sigma $ with $ \ left \ lvert \ sigma \ right \ rvert _ { \ infty } < 1 $ of $ \ overline { \ mathcal { l } } ^ { \ otimes d } $ whose divisor does not have a singular point on the fiber $ \ mathcal { x } _ p $ over any prime $ p < e ^ { \ varepsilon d } $ tends to $ \ zeta _ { \ mathcal { x } } ( 1 + \ dim \ mathcal { x } ) ^ { - 1 } $ as $ d \ rightarrow \ infty $. | arxiv:2002.11179 |
in this paper we discuss the obstacle problem for the $ p $ - laplace operator. we prove optimal growth results for the solution. of particular interest is the point - wise regularity of the solution at free boundary points. the most surprising result we prove is the one for the $ p $ - obstacle problem : find the smallest $ u $ such that $ $ \ hbox { div } ( | \ nabla u | ^ { p - 2 } \ nabla u ) \ leq 0, \ qquad u \ geq \ phi, \ qquad \ hbox { in } b _ 1, $ $ with $ \ phi \ in c ^ { 1, 1 } ( b _ 1 ) $ and given boundary datum on $ \ partial b _ 1 $. we prove that the solution is uniformly $ c ^ { 1, 1 } $ at free boundary points. similar results are obtained in the case of an inhomogeneity belonging to $ l ^ \ infty $. when applied to the corresponding parabolic problem, these results imply that any solution which is lipschitz in time is $ c ^ { 1, \ frac { 1 } { p - 1 } } $ in the spatial variables. | arxiv:1402.4953 |
main - sequence intermediate - mass stars present a radiative envelope that supports internal gravity waves ( igws ). excited at the boundary with the convective core, igws propagate towards the stellar surface and are suspected to impact physical processes such as rotation and chemical mixing. using the fully compressible time - implicit code music, we study igws in two - dimensional simulations of a zero - age - main - sequence 5 solar mass star model up to 91 \ % of the stellar radius with different luminosity and radiative diffusivity enhancements. our results show that low frequency waves excited by core convection are strongly impacted by radiative effects as they propagate. this impact depends on the radial profile of radiative diffusivity which increases by almost 5 orders of magnitude between the centre of the star and the top of the simulation domain. in the upper layers of the simulation domain, we observe an increase of the temperature. our study suggests that this is due to heat added in these layers by igws damped by radiative diffusion. we show that non - linear effects linked to large amplitude igws may be relevant just above the convective core. both these effects are intensified by the artificial enhancement of the luminosity and radiative diffusivity, with enhancement factors up to $ 10 ^ 4 $ times the realistic values. our results also highlight that direct comparison between numerical simulations with enhanced luminosity and observations must be made with caution. finally, our work suggests that thermal effects linked to the damping of igws could have a non - negligible impact on stellar structure. | arxiv:2304.02508 |
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