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we define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway : one which is on in the presence of certain catalysts and off in their absence. we show that examples of catalytic networks include synthetic dna molecular circuits that have been shown to perform signal amplification and molecular logic. recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. our main theorem is that all weakly - reversible networks with critical siphons are catalytic. consequently, we obtain new proofs for the persistence of atomic event - systems of adleman et al., and normal networks of gnacadja. we define autocatalytic networks, and conjecture that a weakly - reversible reaction network has critical siphons if and only if it is autocatalytic. | arxiv:1006.3627 |
we reply to nathan isgur ' s critique that is directed at some of the conclusions drawn from the lattice simulation of valence qcd, regarding the valence quark model and effective chiral theories. | arxiv:hep-lat/9912049 |
matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of nonlinear dynamic behavior ( e. g. through normal forms ). in this paper we will argue that the use of the koopman operator and its spectrum is particularly well suited for this endeavor, both in theory, but also especially in view of recent data - driven algorithm developments. we believe, and document through illustrative examples, that this can nontrivially extend the use and applicability of the koopman spectral theoretical and computational machinery beyond modeling and prediction, towards what can be considered as a systematic discovery of " cole - hopf - type " transformations for dynamics. | arxiv:1712.07144 |
pg1302 - 102 is thought to be a supermassive binary black hole ( bbh ) system according to the periodical variations of its optical and uv photometry, which may be interpreted as being due to the relativistic doppler boosting of the emission mainly from the disk around the secondary black hole ( bh ) modulated by its orbital motion. in this paper, we investigate several broad emission lines of pg1302 - 102 using archived uv spectra obtained by iue, galex, and hubble, to reveal the broad - line region ( blr ) emission properties of this bbh system under the doppler boosting scenario. we find that the broad lines ly $ \ alpha $, nv, civ, and ciii ] all show gaussian profiles, and none of these lines exhibits obvious periodical variation. adopting a simple model for the blr, we perform markov chain monte carlo fittings to these broad lines, and find that the blr must be viewed at an orientation angle of $ \ sim33 ^ { \ circ } $, close to face - on. if the doppler boosting interpretation is correct, then the blr is misaligned with the bbh orbital plane by an angle of $ \ sim51 ^ \ circ $, which suggests that the doppler boosted continuum variation has little effect on the broad - line emission and thus does not lead to periodical line variation. we further discuss the possible implications for such a blr configuration with respect to the bbh orbital plane. | arxiv:2010.07512 |
we introduce data structures for solving robust regression through stochastic gradient descent ( sgd ) by sampling gradients with probability proportional to their norm, i. e., importance sampling. although sgd is widely used for large scale machine learning, it is well - known for possibly experiencing slow convergence rates due to the high variance from uniform sampling. on the other hand, importance sampling can significantly decrease the variance but is usually difficult to implement because computing the sampling probabilities requires additional passes over the data, in which case standard gradient descent ( gd ) could be used instead. in this paper, we introduce an algorithm that approximately samples $ t $ gradients of dimension $ d $ from nearly the optimal importance sampling distribution for a robust regression problem over $ n $ rows. thus our algorithm effectively runs $ t $ steps of sgd with importance sampling while using sublinear space and just making a single pass over the data. our techniques also extend to performing importance sampling for second - order optimization. | arxiv:2207.07822 |
in the framework of supersymmetric grand unified theories ( susy guts ), the universe undergoes a cascade of symmetry breakings, during which topological defects can be formed. we address the question of the probability of cosmic string formation after a phase of hybrid inflation within a large number of models of susy guts in agreement with particle and cosmological data. we show that cosmic strings are extremely generic and should be used to relate cosmology and high energy physics. this conclusion is employed together with the wmap cmb data to strongly constrain susy hybrid inflation models. f - term and d - term inflation are studied in the susy and minimal sugra framework. they are both found to agree with data but suffer from fine tuning of their superpotential coupling ( \ lambda \ lesssim 3 \ times 10 ^ ( - 5 ) or less ). mass scales of inflation are also constrained to be less than m \ lesssim 3 \ times 10 ^ ( 15 ) gev. | arxiv:hep-ph/0603169 |
this work proposes convolutional - sparse - coded dynamic mode decomposition ( csc - dmd ) by unifying extended dynamic mode decomposition ( edmd ) and convolutional sparse coding. edmd is a data driven analysis method for describing a nonlinear dynamical system with a linear time - evolution equation. compared with existing edmd methods, csc - dmd has an advantage of reflecting spatial structure of the target. as an example, the proposed method is applied to river bed shape estimation from the water surface observation. the estimation problem is reduced to sparsity - aware restoration with a hard constraint, which is given by the csc - dmd prediction, where the algorithm is derived by the primal - dual splitting method. a time series set of water surface and bed shape measured through an experimental river setup is used to train and test the system. from the result, the significance of the proposed method is verified. | arxiv:1811.07281 |
we report on coherent emission of the neutral exciton state in a single semiconductor self - assembled inas / gaas quantum dot embedded in a one - dimensional waveguide, under resonant picosecond pulsed excita - tion. direct measurements of the radiative lifetime and coherence time are performed as a function of excitation power and temperature. the characteristic damping of rabi oscillations which is observed, is attributed to an excitation - induced dephasing due to a resonant coupling between the emitter and the acoustic phonon bath of the matrix. other sources responsible for the decrease of the coherence time have been evidenced, in particular an enhancement of the radiative recombination rate due to the resonant strong coupling between the dot and the one - dimensional optical mode. as a consequence, the emission couples very efficiently into the waveguide mode leading to an additional relaxation term of the excited state population. | arxiv:1304.4756 |
we developed theory of particle acceleration inside the relativistic rotating electron - positron force - free jet with spiral magnetic field. we considered perturbation of stationary magnetic field structure and found that acceleration takes place in the regions where the alfven resonant condition with the eigenmodes in the jet is fulfilled. acceleration process and synchrotron losses combined together form power law energy spectrum of ultrarelativistic electrons and positrons with index between 2 and 3 depending upon initial energy of injected particles. synchrotron emission of these electrons and positrons in spiral magnetic field of rotating force - free jet has been calculated. polarization properties of the radiation has been obtained and compared with existing vlbi polarization measurements of parsec - scale jets in bl lac sources and quasars. our results give explanation of observed bimodality in alignment between electric field vector and jet axis. degree of polarization and velocity of observed proper motion of bright knots depend upon angular rotational velocity of the jet. thus, comparing them to each other, we can estimate angular rotational velocity in jets. we obtain that the fact, that generally in bl lac objects electric field vector is oriented parallel to the jet axis while in quasars perpendicular to the jet axis, may be due to intrinsically larger angular rotational velocity and large winding of magnetic field in bl lac jets than in quasar jets. | arxiv:astro-ph/9704046 |
we focus on the task of approximating the optimal value function in deep reinforcement learning. this iterative process is comprised of solving a sequence of optimization problems where the loss function changes per iteration. the common approach to solving this sequence of problems is to employ modern variants of the stochastic gradient descent algorithm such as adam. these optimizers maintain their own internal parameters such as estimates of the first - order and the second - order moments of the gradient, and update them over time. therefore, information obtained in previous iterations is used to solve the optimization problem in the current iteration. we demonstrate that this can contaminate the moment estimates because the optimization landscape can change arbitrarily from one iteration to the next one. to hedge against this negative effect, a simple idea is to reset the internal parameters of the optimizer when starting a new iteration. we empirically investigate this resetting idea by employing various optimizers in conjunction with the rainbow algorithm. we demonstrate that this simple modification significantly improves the performance of deep rl on the atari benchmark. | arxiv:2306.17833 |
automated market makers, first popularized by hanson ' s logarithmic market scoring rule ( or lmsr ) for prediction markets, have become important building blocks, called ' primitives, ' for decentralized finance. a particularly useful primitive is the ability to measure the price of an asset, a problem often known as the pricing oracle problem. in this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers ( or cfmms ) which includes existing popular market makers such as uniswap, balancer, and curve, whose yearly transaction volume totals to billions of dollars. we give sufficient conditions such that, under fairly general assumptions, agents who interact with these constant function market makers are incentivized to correctly report the price of an asset and that they can do so in a computationally efficient way. we also derive several other useful properties that were previously not known. these include lower bounds on the total value of assets held by cfmms and lower bounds guaranteeing that no agent can, by any set of trades, drain the reserves of assets held by a given cfmm. | arxiv:2003.10001 |
in this paper we do a comparative presentation of the linear isotropic cosserat elastic model from two perspectives : the classical mindlin - eringen - nowacki description in terms of a microrotation vector and a new formulation in terms of a skew - symmetric matrix and a curvature energy in dislocation form. we provide the reader with an alternative representation of the energy for the isotropic cosserat model to ease the comparison with the relaxed micromorphic model and the geometrically nonlinear cosserat elastic model. | arxiv:2206.02473 |
wasserstein distance, especially among symmetric positive - definite matrices, has broad and deep influences on development of artificial intelligence ( ai ) and other branches of computer science. a natural idea is to describe the geometry of $ spd \ left ( n \ right ) $ as a riemannian manifold endowed with the wasserstein metric. in this paper, by involving the fiber bundle, we obtain explicit expressions for some locally geometric quantities, including geodesics, exponential maps, the riemannian connection, jacobi fields and curvatures. furthermore, we discuss the behaviour of geodesics and prove that the manifold is globally geodesic convex with non - negative curvatures but no conjugate pair and cut locus. according to arithmetic estimates, we find curvatures can be controlled by the minimal eigenvalue. | arxiv:2012.07106 |
dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. we formalized these structures and several fundamental properties, including number theoretic finiteness results for class groups, in the lean prover as part of the mathlib mathematical library. this paper describes the formalization process, noting the idioms we found useful in our development and mathlib ' s decentralized collaboration processes involved in this project. | arxiv:2102.02600 |
we study the tunneling current between two counterpropagating edge modes described by chiral luttinger liquids when the tunneling takes place along an extended region. we compute this current perturbatively by using a tunnel hamiltonian. our results apply to the case of a pair of different two - dimensional electron gases in the fractional quantum hall regime separated by a barrier, e. g. electron tunneling. we also discuss the case of strong interactions between the edges, leading to nonuniversal exponents even in the case of integer quantum hall edges. in addition to the expected nonlinearities due to the luttinger properties of the edges, there are additional interference patterns due to the finite length of the barrier. | arxiv:cond-mat/0502092 |
this paper considers the equivalence problem for quasi - cyclic codes over finite fields. the results obtained are used to construct isodual quasi - cyclic codes. | arxiv:1607.07798 |
in this article we explain the buium - - coleman approach to the manin - - mumford conjecture, and outline its generalisations. as an illustration, we give a $ p $ - adic proof of a theorem of bombieri, masser and zannier on curves in tori. | arxiv:2504.10611 |
we carry out a detailed study of the role of electronic interaction on $ p $ oxygen orbitals in a mott insulator oxide ( uo $ _ 2 $ ) and a charge transfer oxide ( tio $ _ 2 $ ). first, we calculate values of effective interactions \ uff, \ upp { } and $ u _ { fp } $ in uo $ _ 2 $ and \ udd { }, \ upp { } and $ u _ { dp } $ in tio $ _ 2 $. second, we analyze the role of electronic interactions \ upp { } on $ p $ orbitals of oxygen in spectral and structural properties. finally, we show that this role depends strongly on the definition of correlated orbitals and that using wannier functions leads to more physical results for spectral and structural properties. | arxiv:2207.14137 |
new distributions are presented which allow di - photon + jet events to be clearly separated into three classes of events based on the $ p _ { t } $ of the final state particles and their separation $ r $ = $ \ sqrt { ( \ delta y ) ^ { 2 } + ( \ delta \ phi ) ^ { 2 } } $. the analysis used can easily be extended to the case of di - jet + photon. | arxiv:hep-ph/9507468 |
in the search for novel materials for vacuum electron sources, multi - alkali antimonides and in particular sodium - potassium - antimonides have been recently regarded as especially promising due to their favorable electronic and optical properties. in the framework of density - functional theory and many - body perturbation theory, we investigate the electronic structure and the dielectric response of two representative members of this family, namely na $ _ 2 $ ksb and nak $ _ 2 $ sb. we find that both materials have a direct gap, which is on the order of 1. 5 ev in na $ _ 2 $ ksb and 1. 0 ev in nak $ _ 2 $ sb. in either system, valence and conduction bands are dominated by sb states with p - and s - character, respectively. the imaginary part of the dielectric function, computed upon explicit inclusion of electron - hole interactions to characterize the optical response of the materials, exhibits maxima starting from the near - infrared region, extending up to the visible and the ultraviolet band. with our analysis, we clarify that the lowest - energy excitations are non - excitonic in nature and that their binding energy is on the order of 100 mev. our results confirm the potential of na $ _ 2 $ ksb and nak $ _ 2 $ sb as photoemissive materials for vacuum electron sources, photomultipliers, and imaging devices. | arxiv:2104.08513 |
measurements of the magnetization under high hydrostatic pressure ( up to 10. 2 kbar ) in yba _ 2cu _ 4o _ 8 were carried out. from the scaling analysis of the magnetization data the pressure induced shifts of the transition temperature t _ c, the volume v and the anisotropy \ gamma have been obtained. it was shown that the pressure induced relative shift of t _ c mirrors essentially that of the anisotropy. this observation uncovers a novel generic property of anisotropic type ii superconductors, that inexistent in the isotropic case. | arxiv:cond-mat/0502576 |
we consider the one - dimensional schr \ " odinger equation $ - f ' ' + q _ \ alpha f = ef $ on the positive half - axis with the potential $ q _ \ alpha ( r ) = ( \ alpha - 1 / 4 ) r ^ { - 2 } $. it is known that the value $ \ alpha = 0 $ plays a special role in this problem : all self - adjoint realizations of the formal differential expression $ - \ partial ^ 2 _ r + q _ \ alpha ( r ) $ for the hamiltonian have infinitely many eigenvalues for $ \ alpha < 0 $ and at most one eigenvalue for $ \ alpha \ geq 0 $. we find a parametrization of self - adjoint boundary conditions and eigenfunction expansions that is analytic in $ \ alpha $ and, in particular, is not singular at $ \ alpha = 0 $. employing suitable singular titchmarsh - - weyl $ m $ - functions, we explicitly find the spectral measures for all self - adjoint hamiltonians and prove their smooth dependence on $ \ alpha $ and the boundary condition. using the formulas for the spectral measures, we analyse in detail how the " phase transition " through the point $ \ alpha = 0 $ occurs for both the eigenvalues and the continuous spectrum of the hamiltonians. | arxiv:2001.06128 |
in this paper, we prove that every graph with average degree at least $ s + t + 2 $ has a vertex partition into two parts, such that one part has average degree at least $ s $, and the other part has average degree at least $ t $. this solves a conjecture of cs \ ' { o } ka, lo, norin, wu and yepremyan. | arxiv:2202.08123 |
some previously published expressions for the perturbation of light by gravitational waves exhibit pathological behaviour in the limit of parallel propagation. we show that this is caused by similarly pathological initial or boundary data and can thus be remedied by implementing better - behaved initial conditions. | arxiv:2112.05784 |
spectroscopic follow - up of dozens of transiting planets has revealed the degree of alignment between the equators of stars and the orbits of the planets they host. here we determine a method, applicable to spotted stars, that can reveal the same information from the photometric discovery data, with no need for follow - up. a spot model fit to the global light curve, parametrized by the spin orientation of the star, predicts when the planet will transit the spots. observing several spot crossings during different transits then leads to constraints on the spin - orbit alignment. in cases where stellar spots are small, the stellar inclination, and hence the true alignment, rather than just the sky projection, can be obtained. this method has become possible with the advent of space telescopes such as corot and kepler, which photometrically monitor transiting planets over a nearly continuous, long time baseline. we apply our method to corot - 2, and find the projected spin - orbit alignment angle, lambda = 4. 7 deg + / - 12. 3 deg, in excellent agreement with a previous determination that employed the rossiter - mclaughlin effect. the large spots of the parent star, corot - 2, limit our precision on the stellar inclination : i _ s = 84 deg + / - 36 deg, where i _ s < 90 deg ( > 90 deg ) indicates the rotation axis is tilted towards ( away from ) the line of sight. | arxiv:1107.2106 |
we propose a class of interleavers for a novel deep neural network ( dnn ) architecture that uses algorithmically pre - determined, structured sparsity to significantly lower memory and computational requirements, and speed up training. the interleavers guarantee clash - free memory accesses to eliminate idle operational cycles, optimize spread and dispersion to improve network performance, and are designed to ease the complexity of memory address computations in hardware. we present a design algorithm with mathematical proofs for these properties. we also explore interleaver variations and analyze the behavior of neural networks as a function of interleaver metrics. | arxiv:1711.06935 |
we present the first numerical calculation of the 4d euclidean spin foam vertex amplitude for vertices with hypercubic combinatorics. concretely, we compute the amplitude for coherent boundary data peaked on cuboid and frustum shapes. we present the numerical algorithms to explicitly compute the vertex amplitude and compare the results in different cases to the semi - classical approximation of the amplitude. overall we find good qualitative agreement of the amplitudes and evidence of convergence of the asymptotic formula to the full amplitude already at fairly small spins, yet also differences in the frequency of oscillations and a phase shift absent in the 4 - simplex case. however, due to rapidly growing numerical costs, we cannot reach sufficiently high spins to prove agreement of both amplitudes. lastly, this setup allows us to explore non - uniform vertex amplitudes, where some representations are small while others are large ; we find indications that scenarios might exist in which the semi - classical amplitude is a valid approximation even if some spins remain small. this suggests that the transition of the quantum to the semi - classical regime ( for a single vertex amplitude ) is intricate. | arxiv:2201.09902 |
the spinorial degrees of freedom of two or more spacelike separated dirac particles are considered and a method for constructing mixed polynomials that are invariant under the spinor representations of the local proper orthochronous lorentz groups is described. the method is an extension of the method for constructing homogeneous polynomials introduced in [ phys. rev. a 105, 032402 ( 2022 ), arxiv : 2103. 07784 ] and [ ann. phys. ( n. y. ) 457, 169410 ( 2023 ), arxiv : 2105. 07503 ]. the mixed polynomials constructed by this method are identically zero for all product states. therefore they are considered indicators of the spinor entanglement of dirac particles. mixed polynomials can be constructed to indicate spinor entanglement that involves all the particles, or alternatively to indicate spinor entanglement that involves only a proper subset of the particles. it is shown that the mixed polynomials can indicate some types of spinor entanglement that involves all the particles but cannot be indicated by any homogeneous locally lorentz invariant polynomial. for the case of two dirac particles mixed polynomials of bidegree ( 2, 2 ) and bidegree ( 3, 1 ) are constructed. for the case of three dirac particles mixed polynomials of bidegree ( 2, 2 ), bidegree ( 3, 1 ) and bidegree ( 3, 3 ) are constructed. the relations of the polynomials constructed for two and three dirac particles to the polynomial spin entanglement indicators for two and three non - relativistic spin - $ \ frac { 1 } { 2 } $ particles are described. moreover, the constructed polynomial indicators of spinor entanglement are in general not invariant under local time evolutions of the particles but evolve dynamically and we discuss how to describe this dynamical evolution. | arxiv:2308.00896 |
we study the physics of hard - core bosons with unfrustrated hopping ( t ) and nearest - neighbor repulsion ( v ) on the three dimensional pyrochlore lattice. at half - filling, we demonstrate that the small v / t superfluid state eventually becomes unstable at large enough v / t to an unusual insulating state which displays no broken lattice translation symmetry. equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the coulomb phase of a u ( 1 ) lattice gauge theory, allowing us to identify this insulator with a u ( 1 ) fractionalized mott - insulating state. the possibility of observing this phase in suitably designed atom - trap experiments with ultracold atoms is also discussed, as are specific experimental signatures. | arxiv:cond-mat/0702029 |
d. calaque, k. ebrahimi - fard and d. manchon have recently defined a hopf algebra by introducing a new coproduct on a commutative algebra of rooted forests. the space of primitive elements of the graded dual is endowed with a left pre - lie product defined in terms of insertion of a tree inside another. in this work we prove a ` ` derivation ' ' relation between this pre - lie structure and the left pre - lie product defined by grafting. | arxiv:0811.2153 |
cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system - - our universe. modern cosmological probes increasingly rely on measurements of the small - scale structure, and the only way to accurately model physical behavior on those scales, roughly 65 mpc / h or smaller, is via expensive numerical simulations. in this paper, we provide a detailed description of a novel statistical framework for obtaining accurate parameter constraints by combining observations with a very limited number of cosmological simulations. the proposed framework utilizes multi - output gaussian process emulators that are adaptively constructed using bayesian optimization methods. we compare several approaches for constructing multi - output emulators that enable us to take possible inter - output correlations into account while maintaining the efficiency needed for inference. using lyman alpha forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer - - - by a factor of a few in lyman alpha p ( k ) case considered here - - - simulations compared to the emulation based on latin hypercube sampling, and that the method is more robust in reconstructing parameters and their bayesian credible intervals. | arxiv:1905.07410 |
the structure, formation and evolution of the universe were some of the main topics in the scientific debates during the 17th and 18th centuries in europe. they involved novel ideas on the cosmos, which concerned aspects that were not considered before so emphatically, and which were fundamental for the future development of astronomy. this paper presents a brief account of several milestones within the gradual definition of pre - galactic systems : the historical role of the tradition of the plurality of worlds, the significance of descartes, and the introduction of the milky way and nebulae in the discourses around the cosmic structure. | arxiv:1301.7317 |
the pierre auger observatory is the world ' s largest cosmic ray observatory. our current exposure reaches nearly 40, 000 km $ ^ 2 $ str and provides us with an unprecedented quality data set. the performance and stability of the detectors and their enhancements are described. data analyses have led to a number of major breakthroughs. among these we discuss the energy spectrum and the searches for large - scale anisotropies. we present analyses of our x $ _ { max } $ data and show how it can be interpreted in terms of mass composition. we also describe some new analyses that extract mass sensitive parameters from the 100 % duty cycle sd data. a coherent interpretation of all these recent results opens new directions. the consequences regarding the cosmic ray composition and the properties of uhecr sources are briefly discussed. | arxiv:1310.4620 |
we report an anomalous temperature - induced transition in thermal conductivity in germanene monolayer around a critical temperature $ t _ c = 350 \, \ text { k } $. equilibrium molecular dynamics simulations reveal a transition from $ \ kappa \ sim t ^ { - 2 } $ scaling below $ t _ c $ to $ \ kappa \ sim t ^ { - 1 / 2 } $ above, contrasting with conventional $ \ kappa \ sim t ^ { - 1 } $ behavior. this anomalous scaling correlates with long - scale characteristics timescale $ \ tau _ 2 $ obtained from double exponential fitting of heat current autocorrelation function. phonon mode analysis using normal mode decomposition indicates that a redshift in ta phonons reduces the acoustic - optical phonon gap, enhancing the phonon - phonon scattering and driving the anomalous scaling behavior. moreover, non equilibrium simulations find a convergent thermal conductivity of germanene with sample size, in agreement with mode coupling theory, owing to high scattering of za phonons due to the inherent buckling of germanene. | arxiv:2411.14197 |
the goal of this work is to provide a viable solution based on reinforcement learning for traffic signal control problems. although the state - of - the - art reinforcement learning approaches have yielded great success in a variety of domains, directly applying it to alleviate traffic congestion can be challenging, considering the requirement of high sample efficiency and how training data is gathered. in this work, we address several challenges that we encountered when we attempted to mitigate serious traffic congestion occurring in a metropolitan area. specifically, we are required to provide a solution that is able to ( 1 ) handle the traffic signal control when certain surveillance cameras that retrieve information for reinforcement learning are down, ( 2 ) learn from batch data without a traffic simulator, and ( 3 ) make control decisions without shared information across intersections. we present a two - stage framework to deal with the above - mentioned situations. the framework can be decomposed into an evolution strategies approach that gives a fixed - time traffic signal control schedule and a multi - agent off - policy reinforcement learning that is capable of learning from batch data with the aid of three proposed components, bounded action, batch augmentation, and surrogate reward clipping. our experiments show that the proposed framework reduces traffic congestion by 36 % in terms of waiting time compared with the currently used fixed - time traffic signal plan. furthermore, the framework requires only 600 queries to a simulator to achieve the result. | arxiv:2005.09624 |
we propose a framework to model ferroelectric negative capacitance : electrostatic micro electro mechanical systems ( mems ) hybrid actuators and analyze their dynamic ( step input ) response. using this framework, we report the first proposal for reduction in the dynamic pull - in and pull - out voltages of the hybrid actuators due to the negative capacitance of the ferroelectric. the proposed model also reveals the effect of ferroelectric thickness on the dynamic pull - in and pull - out voltages and the effect of ferroelectric damping on the energy dissipated during actuation. we infer from our analysis that the hybrid actuators are better than the standalone mems actuators in terms of operating voltage and energy dissipation. further, we show that one can trade - off a small part of the reduction in actuation voltage to achieve identical pull - in times in the hybrid and standalone mems actuators, while still consuming substantially lower energy in the former as compared to the latter. the circuit compatibility of the proposed hybrid actuator model makes it suitable for analysis and evaluation of various heterogeneous systems consisting of hybrid mems actuators and other electronic devices. | arxiv:1904.12808 |
the nonlocal chiral effective theory is applied to investigate the electromagnetic and strange form factors of nucleon. the bubble and tadpole diagrams are included in the calculation. with the contributions from bubble and tadpole diagrams, the obtained electromagnetic form factors are close to the results without these contributions as long as the low energy constants $ c _ 1 $ and $ c _ 2 $ are properly chosen, while the magnitudes of strange form factors become larger. both the electromagnetic and strange form factors are still in good agreement with the experimental data. | arxiv:2210.08489 |
we report results from our monitoring of the bl lac object mrk 421 in the near - ir $ j $ band. the observations, aimed at studying the intraday variability ( idv ) of the object, were carried out systematically over an extended ( and near - continuous ) period of eight nights from the 1. 2m mount abu infrared telescope, india. there are limited studies for mrk 421 in the $ j $ band for such an extended period. the observation epoch for this study ( 25 february - 5 march 2003 ) was chosen to significantly overlap other concurrent studies of mrk 421 in the x - ray / $ \ gamma $ - ray regions being conducted using the rossi x - ray timing explorer ( rxte ) and the solar tower atmospheric cherenkov effect experiment ( stacee ). hence these results could be useful for a multi - wavelength analysis of the variability behavior of mrk 421. we find that mrk 421 was quite active during the observed period and showed significant idv and short term variability. a maximum variation of 0. 89 magnitudes is seen over the entirety of the observed period. flaring activity, with typical brightness variations of $ \ sim 0. 4 $, are also seen on several occasions. the extent of the variability observed by us is compared with the results of other similar studies of mrk 421 in the $ j $ band. | arxiv:astro-ph/0405186 |
we show that when the qcd axion is directly coupled to quarks with $ c _ q / f \, \ partial _ \ mu a \, \ bar { q } \ gamma ^ \ mu \ gamma ^ 5 q $, such as in dfsz models, the dominant production mechanism in the early universe at temperatures $ 1 \, { \ rm gev } \ lesssim t \ lesssim 100 \, { \ rm gev } $ is obtained via $ q \ bar { q } \ leftrightarrow g a $ and $ q g \ leftrightarrow q a $, where $ g $ are gluons. different heavy quarks $ q _ i $ can produce a thermal axion background that decouples at a temperature $ t _ i $ : ( 1 ) top quark at $ t _ t \ lesssim 100 \, { \ rm gev } $ for $ f / c _ t \ lesssim 3 \ times 10 ^ 8 { \ rm gev } $ ; ( 2 ) bottom quark at $ t _ b \ lesssim m _ b $, for $ f / c _ b \ lesssim 8 \ times 10 ^ { 7 } { \ rm gev } $ ; ( 3 ) charm quark at $ t _ c \ lesssim m _ c $ for $ f / c _ c \ lesssim 5 \ times 10 ^ { 7 } { \ rm gev } $. each of these cases corresponds to a contribution to the effective number of relativistic degrees of freedom, in the windows given by $ 0. 027 \ leq \ delta n _ \ text { eff } \ leq 0. 031 $, $ 0. 037 \ leq \ delta n _ \ text { eff } \ leq 0. 039 $ and $ 0. 039 \ leq \ delta n _ \ text { eff } $, respectively. these contributions are larger than the one obtained when thermalization happens only above the electroweak phase transition, $ \ delta n _ { \ rm eff } \ lesssim 0. 027 $, and are within reach of future cmb s4 experiments, thus opening an alternative window to detect the axion and to test the early universe at such temperatures. | arxiv:1801.06090 |
preterm neonates are highly likely to suffer from ventriculomegaly, a dilation of the cerebral ventricular system ( cvs ). this condition can develop into life - threatening hydrocephalus and is correlated with future neuro - developmental impairments. consequently, it must be detected and monitored by physicians. in clinical routing, manual 2d measurements are performed on 2d ultrasound ( us ) images to estimate the cvs volume but this practice is imprecise due to the unavailability of 3d information. a way to tackle this problem would be to develop automatic cvs segmentation algorithms for 3d us data. in this paper, we investigate the potential of 2d and 3d convolutional neural networks ( cnn ) to solve this complex task and propose to use compositional pattern producing network ( cppn ) to enable the cnns to learn cvs location. our database was composed of 25 3d us volumes collected on 21 preterm nenonates at the age of $ 35. 8 \ pm 1. 6 $ gestational weeks. we found that the cppn enables to encode cvs location, which increases the accuracy of the cnns when they have few layers. accuracy of the 2d and 3d cnns reached intraobserver variability ( iov ) in the case of dilated ventricles with dice of $ 0. 893 \ pm 0. 008 $ and $ 0. 886 \ pm 0. 004 $ respectively ( iov = $ 0. 898 \ pm 0. 008 $ ) and with volume errors of $ 0. 45 \ pm 0. 42 $ cm $ ^ 3 $ and $ 0. 36 \ pm 0. 24 $ cm $ ^ 3 $ respectively ( iov = $ 0. 41 \ pm 0. 05 $ cm $ ^ 3 $ ). 3d cnns were more accurate than 2d cnns in the case of normal ventricles with dice of $ 0. 797 \ pm 0. 041 $ against $ 0. 776 \ pm 0. 038 $ ( iov = $ 0. 816 \ pm 0. 009 $ ) and volume errors of $ 0. 35 \ pm 0. 29 $ cm $ ^ 3 $ against $ 0. 35 \ pm 0. 24 $ cm $ ^ 3 $ ( iov = $ 0. 2 \ pm 0. 11 $ cm $ ^ 3 $ ). the best segmentation time of volumes of size $ 320 \ times 320 \ | arxiv:2012.03014 |
in this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective noether ' s irreducibility theorem given by ruppert. with this approach, some new effective results are obtained. in particular, we show that the reduction modulo p of the spectrum of a given integer multivariate rational function r coincides with the spectrum of the reduction of r modulo p for p a prime integer greater or equal to an explicit bound. this bound is given in terms of the degree, the height and the number of variables of r. with the same strategy, we also study the decomposability of r modulo p. some similar explicit results are also provided for the case of polynomials with coefficients in a polynomial ring. | arxiv:0906.2925 |
we present an approach to studying the casimir effects by means of the effective theory. an essential point of our approach is replacing the mirror separation into the size of space s ^ 1 in the adiabatic approximation. it is natural to identify the size of space s ^ 1 with the scale factor of the robertson - walker - type metric. this replacement simplifies the construction of a class of effective models to study the casimir effects. to check the validity of this replacement we construct a model for a scalar field coupling to the two - dimensional gravity and calculate the casimir effects by the effective action for the variable scale factor. our effective action consists of the classical kinetic term of the mirror separation and the quantum correction derived by the path - integral method. the quantum correction naturally contains both the casimir energy term and the back - reaction term of the dynamical casimir effect, the latter of which is expressed by the conformal anomaly. the resultant effective action describes the dynamical vacuum pressure, i. e., the dynamical casimir force. we confirm that the force depends on the relative velocity of the mirrors, and that it is always attractive and stronger than the static casimir force within the adiabatic approximation. | arxiv:hep-th/9904193 |
we introduce a new algorithm for finding stable matchings in multi - sided matching markets. our setting is motivated by a phd market of students, advisors, and co - advisors, and can be generalized to supply chain networks viewed as $ n $ - sided markets. in the three - sided phd market, students primarily care about advisors and then about co - advisors ( consistent preferences ), while advisors and co - advisors have preferences over students only ( hence they are cooperative ). a student must be matched to one advisor and one co - advisor, or not at all. in contrast to previous work, advisor - student and student - co - advisor pairs may not be mutually acceptable ( e. g., a student may not want to work with an advisor or co - advisor and vice versa ). we show that three - sided stable matchings always exist, and present an algorithm that, in time quadratic in the market size ( up to log factors ), finds a three - sided stable matching using any two - sided stable matching algorithm as matching engine. we illustrate the challenges that arise when not all advisor - co - advisor pairs are compatible. we then generalize our algorithm to $ n $ - sided markets with quotas and show how they can model supply chain networks. finally, we show how our algorithm outperforms the baseline given by [ danilov, 2003 ] in terms of both producing a stable matching and a larger number of matches on a synthetic dataset. | arxiv:2102.11834 |
this paper generalizes the notion of geometric curves such as hyperbolas and ellipses to more general vector spaces with an associated inner product. this is done by generalizing the definition in terms of loci and foci of said curves in euclidean geometry to a general vector space with a real inner product, through which a norm can be induced. through this generalization and focusing on the curves that are obtained through linear combinations of norms, we explore some properties of said curves. specifically, we explore the addition of vectors in the curve, and in what other curves this addition can be found in relation to the original curve. lastly, we observe the effects of applying the isomorphism to the geometric curve in the vector space onto r ^ n, and we compare geometric curves obtained with the same definition in different vector spaces with different norms. | arxiv:2402.17884 |
i ' m presenting a new elegant formulation of the theory of fully nonlinear adiabatic twm ( fna - twm ) in terms of elliptic function here. note that the linear case of sfg and dfg in the undepleted pump approximation described by the fvh representation has been exploited several years ago. for the sake of completeness, i present the pseudo - fvh representation to describe opa. moreover, i ' m trying to display an overview of twm processes and show that both the linear cases, the linear adiabatic sfg ( dfg ) and the linear opa, are only the special cases of my theory. finally i also point out that the geometric image of the so - called adiabatic basis acts as the geodesic line of the generalized bloch sphere. | arxiv:1604.05751 |
in recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental principles and lead to reasoned predictions. even though students have the required knowledge and skills, they are often based on a variety of intuitive reasoning that leads them to wrong conclusions. this paper studies students ' reasoning on science problems through heuristic - analytical thought processes ( system 1 - system 2 ). system 1 operates automatically and quickly with little or no effort and no sense of voluntary control, while system 2 focuses on the demanding mental activities that require it and is slow based on rules. | arxiv:2402.05497 |
slow wave sleep duration and spectral abnormalities are related to both epilepsy and depression, but it is unclear how depressive symptoms in patients with epilepsy are affected by slow wave sleep duration and clinical factors, and how the spectral characteristics of slow wave sleep reflect a potential interaction of epilepsy and depression. long - term video - eeg monitoring was conducted in 51 patients with focal epilepsy, 13 patients with generalized epilepsy, and 9 patients without epilepsy. slow wave sleep segments were manually marked in the eeg and duration as well as eeg power spectra were extracted. depressive symptoms were documented with the beck depression inventory ( bdi ). at least mild depressive symptoms ( bdi > 9 ) were found among 23 patients with focal epilepsy, 5 patients with generalised epilepsy, and 6 patients who had no epilepsy diagnosis. slow wave sleep duration was shorter for patients with at least mild depressive symptoms ( p =. 004 ), independently from epilepsy diagnosis, antiseizure medication, age, and sex. psychoactive medication was associated with longer slow wave sleep duration ( p =. 008 ). frontal sigma band power ( 13 - 15 hz ) during slow wave sleep was higher for patients without epilepsy and without depressive symptoms as compared to patients without depressive symptoms but with focal epilepsy ( p =. 005 ). depressive symptoms affect slow wave sleep duration of patients with epilepsy similarly as in patients without epilepsy. since reduced slow wave sleep can increase the likelihood of seizure occurrence, these results stress the importance of adequate treatment for patients with epilepsy who experience depressive symptoms. | arxiv:2311.01280 |
we establish a min - max estimate on the volume width of a closed riemannian manifold with nonnegative ricci curvature. more precisely, we show that every closed riemannian manifold with nonnegative ricci curvature admits a pl morse function whose level set volume is bounded in terms of the volume of the manifold. as a consequence of this sweep - out estimate, there exists an embedded, closed ( possibly singular ) minimal hypersurface whose volume is bounded in terms of the volume of the manifold. | arxiv:1408.4470 |
the following report introduces ideas augmenting standard long short term memory ( lstm ) architecture with multiple memory cells per hidden unit in order to improve its generalization capabilities. it considers both deterministic and stochastic variants of memory operation. it is shown that the nondeterministic array - lstm approach improves state - of - the - art performance on character level text prediction achieving 1. 402 bpc on enwik8 dataset. furthermore, this report estabilishes baseline neural - based results of 1. 12 bpc and 1. 19 bpc for enwik9 and enwik10 datasets respectively. | arxiv:1607.03085 |
in this paper, we investigate a scalar field brans - dicke cosmological model in lyra ' s geometry which is based on the modifications in geometrical term as well as energy term of einstein ' s field equations. we have examined the validity of proposed cosmological model on observational scale by performing statistical analysis from latest $ h ( z ) $ and sn ia observational data. we find that the estimated values of hubble ' s constant and matter energy density parameter are in agreement with their corresponding values, obtained from recent observations of wmap and plank collaboration. we also derived deceleration parameter, age of the universe and jerk parameter in terms of red - shift and computed its present values. the dynamics of deceleration parameter in derived model of the universe shows a signature flipping from positive to negative value and also indicates that the present universe is in accelerating phase. | arxiv:1909.01998 |
and ] to supply the state or commonwealth with a revenue for the publick services. jean - baptiste say ( 1803 ), distinguishing the subject matter from its public - policy uses, defined it as the science of production, distribution, and consumption of wealth. on the satirical side, thomas carlyle ( 1849 ) coined " the dismal science " as an epithet for classical economics, in this context, commonly linked to the pessimistic analysis of malthus ( 1798 ). john stuart mill ( 1844 ) delimited the subject matter further : the science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object. alfred marshall provided a still widely cited definition in his textbook principles of economics ( 1890 ) that extended analysis beyond wealth and from the societal to the microeconomic level : economics is a study of man in the ordinary business of life. it enquires how he gets his income and how he uses it. thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man. lionel robbins ( 1932 ) developed implications of what has been termed " [ p ] erhaps the most commonly accepted current definition of the subject " : economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses. robbins described the definition as not classificatory in " pick [ ing ] out certain kinds of behaviour " but rather analytical in " focus [ ing ] attention on a particular aspect of behaviour, the form imposed by the influence of scarcity. " he affirmed that previous economists have usually centred their studies on the analysis of wealth : how wealth is created ( production ), distributed, and consumed ; and how wealth can grow. but he said that economics can be used to study other things, such as war, that are outside its usual focus. this is because war has as the goal winning it ( as a sought - after end ), generates both cost and benefits ; and, resources ( human life and other costs ) are used to attain the goal. if the war is not winnable or if the expected costs outweigh the benefits, the deciding actors ( assuming they are rational ) may never go to war ( a decision ) but rather explore other alternatives. economics cannot be defined as the science that studies wealth, war, crime, education, and any other field economic analysis can | https://en.wikipedia.org/wiki/Economics |
from the study of a functional equation of gibbs measures we calculate the limiting free energy of the sherrington - kirkpatrick spin glass model at a particular value of ( low ) temperature. this implies the following lower bound for the ground state energy $ \ epsilon _ 0 $ \ [ \ epsilon _ 0 \ geq - 0. 7833 \ cdots, \ ] close to the replica symmetry breaking and numerical simulations values. | arxiv:0806.1380 |
social networks are quickly becoming the primary medium for discussing what is happening around real - world events. the information that is generated on social platforms like twitter can produce rich data streams for immediate insights into ongoing matters and the conversations around them. to tackle the problem of event detection, we model events as a list of clusters of trending entities over time. we describe a real - time system for discovering events that is modular in design and novel in scale and speed : it applies clustering on a large stream with millions of entities per minute and produces a dynamically updated set of events. in order to assess clustering methodologies, we build an evaluation dataset derived from a snapshot of the full twitter firehose and propose novel metrics for measuring clustering quality. through experiments and system profiling, we highlight key results from the offline and online pipelines. finally, we visualize a high profile event on twitter to show the importance of modeling the evolution of events, especially those detected from social data streams. | arxiv:1907.11229 |
we review some current ideas about tripartite entanglement, the case representing the next level of complexity beyond the simplest one ( though far from trivial ), namely the bipartite. this kind of entanglement has an essential role in the understanding of foundations of quantum mechanics. also, it allows several applications in the fields of quantum information processing and quantum computing. in this paper, we make a revision about the main foundational aspects of tripartite entanglement and we discuss the possibility of using it as a resource to execute quantum protocols. we present some examples of quantum protocols in detail. | arxiv:1909.00862 |
in this paper we consider the so - called toda system in planar domains under dirichlet boundary condition. we show the existence of continua of solutions for which one component is blowing up at a certain number of points. the proofs use singular perturbation methods. | arxiv:1407.8407 |
in nature, the process of cellular growth and differentiation has lead to an amazing diversity of organisms - - algae, starfish, giant sequoia, tardigrades, and orcas are all created by the same generative process. inspired by the incredible diversity of this biological generative process, we propose a generative model, the variational neural cellular automata ( vnca ), which is loosely inspired by the biological processes of cellular growth and differentiation. unlike previous related works, the vnca is a proper probabilistic generative model, and we evaluate it according to best practices. we find that the vnca learns to reconstruct samples well and that despite its relatively few parameters and simple local - only communication, the vnca can learn to generate a large variety of output from information encoded in a common vector format. while there is a significant gap to the current state - of - the - art in terms of generative modeling performance, we show that the vnca can learn a purely self - organizing generative process of data. additionally, we show that the vnca can learn a distribution of stable attractors that can recover from significant damage. | arxiv:2201.12360 |
we present a simple uv completion of atomic dark matter ( adm ) in which heavy right - handed neutrinos decay to induce both dark and lepton number densities. this model addresses several outstanding cosmological problems : the matter / anti - matter asymmetry, the dark matter abundance, the number of light degrees of freedom in the early universe, and the smoothing of small - scale structure. additionally, this realization of adm may reconcile the cogent excess with recently published null results and predicts a signal in the cresst oxygen band. we also find that, due to unscreened long - range interactions, the residual un recombined dark ions settle into a diffuse isothermal halo. | arxiv:1105.2073 |
in response to the gap in considering wind conditions in the bridge inspection using unmanned aerial vehicle ( uav ), this paper proposes a path planning method for uavs that takes into account the influence of wind, based on the simulated annealing algorithm. the algorithm considers the wind factors, including the influence of different wind speeds and directions at the same time on the path planning of the uav. firstly, an environment model is constructed specifically for uav bridge inspection, taking into account the various objective functions and constraint conditions of uavs. a more sophisticated and precise mathematical model is then developed based on this environmental model to enable efficient and effective uav path planning. secondly, the bridge separation planning model is applied in a novel way, and a series of parameters are simulated, including the adjustment of the initial temperature value. the experimental results demonstrate that, compared with traditional local search algorithms, the proposed method achieves a cost reduction of 30. 05 \ % and significantly improves effectiveness. compared to path planning methods that do not consider wind factors, the proposed approach yields more realistic and practical results for uav applications, as demonstrated by its improved effectiveness in simulations. these findings highlight the value of our method in facilitating more accurate and efficient uav path planning in wind - prone environments. | arxiv:2401.10519 |
we present the final results from a targeted search for brown dwarfs with unusual near - infrared colors. from a positional cross - match of sdss, 2mass and wise, we have identified 144 candidate peculiar l and t dwarfs. spectroscopy confirms that 20 of the objects are peculiar or are candidate binaries. nine of the 420 objects in our sample are young ( $ \ lesssim $ 200 myr ; 2. 1 % ) and another 8 ( 1. 9 % ) are unusually red with no signatures of youth. with a spectroscopic $ j - k _ s $ color of 2. 58 $ \ pm $ 0. 11 mag, one of the new objects, the l6 dwarf 2mass j03530419 + 0418193, is among the reddest field dwarfs currently known and is one of the reddest objects with no signatures of youth known to date. we have also discovered another potentially very low gravity object, the l1 dwarf 2mass j00133470 + 1109403, and independently identified the young l7 dwarf 2mass j00440332 + 0228112, first reported by schneider and collaborators. our results confirm that signatures of low gravity are no longer discernible in low to moderate resolution spectra of objects older than $ \ sim $ 200 myr. the 1. 9 % of unusually red l dwarfs that do not show other signatures of youth could be slightly older, up to $ \ sim $ 400 myr. in this case a red $ j - k _ s $ color may be more diagnostic of moderate youth than individual spectral features. however, its is also possible that these objects are relatively metal - rich, and so have an enhanced atmospheric dust content. | arxiv:1708.03688 |
we introduce a zfc method that enables us to build spaces ( in fact special dense subspaces of certain cantor cubes ) in which we have " full control " over all dense subsets. using this method we are able to construct, in zfc, for each uncountable regular cardinal $ \ lambda $ a 0 - dimensional $ t _ 2 $, hence tychonov, space which is $ \ mu $ - resolvable for all $ \ mu < \ lambda $ but not $ \ lambda $ - resolvable. this yields the final ( negative ) solution of a celebrated problem of ceder and pearson raised in 1967 : are $ \ omega $ - resolvable spaces maximally resolvable? this method enables us to solve several other open problems concerning resolvability as well. | arxiv:math/0609090 |
text based games are simulations in which an agent interacts with the world purely through natural language. they typically consist of a number of puzzles interspersed with interactions with common everyday objects and locations. deep reinforcement learning agents can learn to solve these puzzles. however, the everyday interactions with the environment, while trivial for human players, present as additional puzzles to agents. we explore two techniques for incorporating commonsense knowledge into agents. inferring possibly hidden aspects of the world state with either a commonsense inference model comet, or a language model bert. biasing an agents exploration according to common patterns recognized by a language model. we test our technique in the 9to05 game, which is an extreme version of a text based game that requires numerous interactions with common, everyday objects in common, everyday scenarios. we conclude that agents that augment their beliefs about the world state with commonsense inferences are more robust to observational errors and omissions of common elements from text descriptions. | arxiv:2012.02757 |
selfish network creation focuses on modeling real world networks from a game - theoretic point of view. one of the classic models by fabrikant et al. [ podc ' 03 ] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of $ \ alpha $ per edge to minimize their total distance to all other nodes. the model is well - studied but still has intriguing open problems. the most famous conjectures state that the price of anarchy is constant for all $ \ alpha $ and that for $ \ alpha \ geq n $ all equilibrium networks are trees. we introduce a novel technique for analyzing stable networks for high edge - price $ \ alpha $ and employ it to improve on the best known bounds for both conjectures. in particular we show that for $ \ alpha > 4n - 13 $ all equilibrium networks must be trees, which implies a constant price of anarchy for this range of $ \ alpha $. moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees. | arxiv:1710.01782 |
we explore full / partial tidal disruption events ( tdes ) of stars / planets by stellar compact objects ( black holes ; bhs ; or neutron stars ; nss ), which we term micro - tdes. disruption of a star / planet with mass $ m _ { \ star } $ may lead to the formation of a debris disk around the bh / ns. efficient accretion of a fraction $ ( f _ { acc } = 0. 1 $ of the debris may then give rise to bright energetic long ( $ 10 ^ { 3 } - 10 ^ { 4 } \, s $ ), x - ray / gamma - ray flares, with total energies of up to $ ( f _ { acc } / 0. 1 ) \ times10 ^ { 52 } \, ( m _ { \ star } / { 0. 6 \, m _ { \ odot } } ) \, $ ergs, possibly resembling ultra - long grbs / xrfs. the energy of such flares depends on the poorly constrained accretion processes. significantly fainter flares might be produced if most of the disk mass is blown away through strong outflows. we suggest three dynamical origins for such disruptions. in the first, a star / planet is tidally disrupted following a close random encounter with a bh / ns in a dense cluster. we estimate the bh ( ns ) micro - tde rates from this scenario to be few $ \ times10 ^ { - 6 } $ ( few $ \ times10 ^ { - 7 } $ ) $ { \ rm yr } ^ { - 1 } $ per milky - way galaxy. another scenario involves the interaction of wide companions due to perturbations by stars in the field, likely producing comparable but lower rates. finally, a third scenario involves a bh / ns which gain a natal velocity kick at birth, leading to a close encounter with a binary companion and the tidal disruption of that companion. such events could be associated with a supernova, or even with a preceding grb / xrf event, and would likely occur hours to days after the prompt explosion ; the rates of such events could be larger than those obtained from the other scenarios, depending on the preceding complex binary stellar evolution. | arxiv:1602.07698 |
hypergraphs are characterized by complex topological structure, representing higher - order interactions among multiple entities through hyperedges. lately, hypergraph - based deep learning methods to learn informative data representations for the problem of node classification on text - attributed hypergraphs have garnered increasing research attention. however, existing methods struggle to simultaneously capture the full extent of hypergraph structural information and the rich linguistic attributes inherent in the nodes attributes, which largely hampers their effectiveness and generalizability. to overcome these challenges, we explore ways to further augment a pretrained bert model with specialized hypergraph - aware layers for the task of node classification. such layers introduce higher - order structural inductive bias into the language model, thus improving the model ' s capacity to harness both higher - order context information from the hypergraph structure and semantic information present in text. in this paper, we propose a new architecture, hyperbert, a mixed text - hypergraph model which simultaneously models hypergraph relational structure while maintaining the high - quality text encoding capabilities of a pre - trained bert. notably, hyperbert presents results that achieve a new state - of - the - art on five challenging text - attributed hypergraph node classification benchmarks. | arxiv:2402.07309 |
the ord ' s graph is a simple graphical method for displaying frequency distributions of data or theoretical distributions in the two - dimensional plane. its coordinates are proportions of the first three moments, either empirical or theoretical ones. a modification of the ord ' s graph based on proportions of indices of qualitative variation is presented. such a modification makes the graph applicable also to data of categorical character. in addition, the indices are normalized with values between 0 and 1, which enables comparing data files divided into different numbers of categories. both the original and the new graph are used to display grapheme frequencies in eleven slavic languages. as the original ord ' s graph requires an assignment of numbers to the categories, graphemes were ordered decreasingly according to their frequencies. data were taken from parallel corpora, i. e., we work with grapheme frequencies from a russian novel and its translations to ten other slavic languages. then, cluster analysis is applied to the graph coordinates. while the original graph yields results which are not linguistically interpretable, the modification reveals meaningful relations among the languages. | arxiv:1504.03608 |
motivated by the recently demonstrated ability to attach quantum dots to polymers at well defined locations, we propose a condensed phase analog of the ion trap quantum computer : a scheme for quantum computation using chemically assembled semiconductor nanocrystals attached to a linear support. the linear support is either a molecular string ( e. g., dna ) or a nanoscale rod. the phonon modes of the linear support are used as a quantum information bus between the dots. our scheme offers greater flexibiliy in optimizing material parameters than the ion trap method but has additional complications. we discuss the relevant physical parameters, provide a detailed feasibility study, and suggest materials for which quantum computation may be possible with this approach. we find that si is a potentially promising quantum dot material, already allowing 5 - 10 qubits quantum computer to operate with an error threshold of 10 ^ - 3. | arxiv:quant-ph/0105102 |
we prove a lie - algebraic characterization of vector bundle for the lie algebra $ \ mathcal { d } ( e, m ), $ seen as $ { \ rm c } ^ \ infty ( m ) - $ module, of all linear operators acting on sections of a vector bundle $ e \ to m $. we obtain similar result for its lie subalgebra $ \ mathcal { d } ^ 1 ( e, m ) $ of all linear first - order differential operators. thanks to a well - chosen filtration, $ \ mathcal { d } ( e, m ) $ becomes $ \ mathcal { p } ( e, m ) $ and we prove that $ \ mathcal { p } ^ 1 ( e, m ) $ characterizes the vector bundle without the hypothesis of being seen as $ { \ rm c } ^ \ infty ( m ) - $ module. we prove that the lie algebra $ \ mathcal { s } ( \ mathcal { p } ( e, m ) ) $ of symbols of linear operators acting on smooth sections of a vector bundle $ e \ to m, $ characterizes it. to obtain this, we assume that $ \ mathcal { s } ( \ mathcal { p } ( e, m ) ) $ is seen as $ { \ rm c } ^ \ infty ( m ) - $ module. we obtain a similar result with the lie algebra $ \ mathcal { s } ^ 1 ( \ mathcal { p } ( e, m ) ) $ of symbols of first - order linear operators without the hypothesis of being seen as a $ { \ rm c } ^ \ infty ( m ) - $ module. | arxiv:2007.14649 |
we study malliavin differentiability for the solutions of a stochastic differential equation with drift of super - linear growth. assuming we have a monotone drift with polynomial growth, we prove malliavin differentiability of any order. as a consequence of this result, under the h \ " ormander ' s hypothesis we prove that the density of the solution ' s law with respect to the lebesgue measure is infinitely differentiable. to avoid non - integrability problems due to the unbounded drift, we follow an approach based on the concepts of ray absolute continuity and stochastic gate \ ^ aux differentiability. | arxiv:2405.19482 |
we consider the nash equilibrium problem in a partial - decision information scenario. specifically, each agent can only receive information from some neighbors via a communication network, while its cost function depends on the strategies of possibly all agents. in particular, while the existing methods assume undirected or balanced communication, in this paper we allow for non - balanced, directed graphs. we propose a fully - distributed pseudo - gradient scheme, which is guaranteed to converge with linear rate to a nash equilibrium, under strong monotonicity and lipschitz continuity of the game mapping. our algorithm requires global knowledge of the communication structure, namely of the perron - frobenius eigenvector of the adjacency matrix and of a certain constant related to the graph connectivity. therefore, we adapt the procedure to setups where the network is not known in advance, by computing the eigenvector online and by means of vanishing step sizes. | arxiv:2009.04981 |
statistical static timing analysis ( ssta ) is studied from the point of view of mathematical optimization. we present two formulations of the problem of finding the critical path delay distribution that were not known before : ( i ) a formulation of the ssta problem using binary - - integer programming and ( ii ) a practical formulation using geometric programming. for simplicity, we use histogram approximation of the distributions. scalability of the approaches is studied and possible generalizations are discussed. | arxiv:2211.02981 |
we study the quark - gluon mixed condensate g < \ bar { q } sigma g q >, which is another chiral order parameter, using the su ( 3 ) c lattice qcd with the kogut - susskind ( ks ) fermion at the quenched level. we generate 100 gauge configurations on the 16 ^ 4 lattice with \ beta = 6. 0, and measure the mixed condensate at 16 points in each gauge configuration for each current - quark mass of m _ q = 21, 36, 52 mev. from the 1600 data for each m _ q, we find the ratio between the mixed condensate and the quark condensate, m _ 0 ^ 2 = g < \ bar { q } sigma g q > / < \ bar { q } q > \ simeq 2. 5 gev ^ 2 at the lattice scale of 1 / a \ simeq 2 gev in the chiral limit. the large value of the mixed condensate suggests its importance in the operator product expansions in qcd. | arxiv:hep-lat/0212025 |
in this paper we give five gauge - invariant systems of governing equations for first and second order scalar perturbations of flat friedmann - lema \ ^ { i } tre universes that are minimal in the sense that they contain no redundant equations or variables. we normalize the variables so that they are dimensionless, which leads to systems of equations that are simple and ready - to - use. we compare the properties and utility of the different systems. for example, they serve as a starting point for finding explicit solutions for two benchmark problems in cosmological perturbation theory at second order : adiabatic perturbations in the super - horizon regime ( the long wavelength limit ) and perturbations of $ \ lambda $ cdm universes. however, our framework has much wider applicability and serves as a reference for future work in the field. | arxiv:1808.03200 |
comets are primitive objects that formed in the protoplanetary disk, and have been largely preserved over the history of the solar system. however, they are not pristine, and surfaces of cometary nuclei do evolve. in order to understand the extent of their primitive nature, we must define the mechanisms that affect their surfaces and comae. we examine the lightcurve of comet 240p / neat over three consecutive orbits, and investigate three events of significant brightening ( $ \ delta m \ sim - 2 $ mag ). unlike typical cometary outbursts, each of the three events are long - lived, with enhanced activity for at least 3 to 6 months. the third event, observed by the zwicky transient facility, occurred in at least two stages. the anomalous behavior appears to have started after the comet was perturbed by jupiter in 2007, reducing its perihelion distance from 2. 53 to 2. 12 au. we suggest that the brightening events are temporary transitions to a higher baseline activity level, brought on by the increased insolation, which has warmed previously insulated sub - surface layers. the new activity is isolated to one or two locations on the nucleus, indicating that the surface or immediate sub - surface is heterogeneous. further study of this phenomenon may provide insight into cometary outbursts, the structure of the near - surface nucleus, and cometary nucleus mantling. | arxiv:1911.02383 |
in this paper, we consider the problem of repairing a data - trained rectified linear unit ( relu ) neural network ( nn ) controller for a discrete - time, input - affine system. that is we assume that such a nn controller is available, and we seek to repair unsafe closed - loop behavior at one known " counterexample " state while simultaneously preserving a notion of safe closed - loop behavior on a separate, verified set of states. to this end, we further assume that the nn controller has a two - level lattice ( tll ) architecture, and exhibit an algorithm that can systematically and efficiently repair such an network. facilitated by this choice, our approach uses the unique semantics of the tll architecture to divide the repair problem into two significantly decoupled sub - problems, one of which is concerned with repairing the un - safe counterexample - - and hence is essentially of local scope - - and the other of which ensures that the repairs are realized in the output of the network - - and hence is essentially of global scope. we then show that one set of sufficient conditions for solving each these sub - problems can be cast as a convex feasibility problem, and this allows us to formulate the tll repair problem as two separate, but significantly decoupled, convex optimization problems. finally, we evaluate our algorithm on a tll controller on a simple dynamical model of a four - wheel - car. | arxiv:2104.02788 |
human knowledge is made up of the conceptual structures of many communities of interest. in order to establish coherence in human knowledge representation, it is important to enable communication between the conceptual structures of different communities the conceptual structures of any particular community is representable in an ontology. such a ontology provides a formal linguistic standard for that community. however, a standard community ontology is established for various purposes, and makes choices that force a given interpretation, while excluding others that may be equally valid for other purposes. hence, a given representation is relative to the purpose for that representation. due to this relativity of representation, in the larger scope of all human knowledge it is more important to standardize methods and frameworks for relating ontologies than to standardize any particular choice of ontology. the standardization of methods and frameworks is called the semantic integration of ontologies. | arxiv:2404.13782 |
epistasis ( gene - gene interaction ) is crucial to predicting genetic disease. our work tackles the computational challenges faced by previous works in epistasis detection by modeling it as a one - step markov decision process where the state is genome data, the actions are the interacted genes, and the reward is an interaction measurement for the selected actions. a reinforcement learning agent using policy gradient method then learns to discover a set of highly interacted genes. | arxiv:1809.09143 |
kingdomino is introduced as an interesting game for studying game playing : the game is multiplayer ( 4 independent players per game ) ; it has a limited game depth ( 13 moves per player ) ; and it has limited but not insignificant interaction among players. several strategies based on locally greedy players, monte carlo evaluation ( mce ), and monte carlo tree search ( mcts ) are presented with variants. we examine a variation of uct called progressive win bias and a playout policy ( player - greedy ) focused on selecting good moves for the player. a thorough evaluation is done showing how the strategies perform and how to choose parameters given specific time constraints. the evaluation shows that surprisingly mce is stronger than mcts for a game like kingdomino. all experiments use a cloud - native design, with a game server in a docker container, and agents communicating using a rest - style json protocol. this enables a multi - language approach to separating the game state, the strategy implementations, and the coordination layer. | arxiv:1807.04458 |
an experimental and numerical smoothed particle hydrodynamics ( sph ) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin - filled, slender enclosure at low rayleigh numbers ( $ 1. 18 \ leq { \ rm ra } \ leq 242 $ ). both the experiments and the sph calculations were performed for positive ( $ 0. 1 \ leq \ delta t \ leq 10 $ k ) and negative ( $ - 10 \ leq \ delta t \ leq - 0. 1 $ k ) temperature differences between the source and the surrounding fluid. in all cases a pair of steady, counter - rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for $ \ delta t > 0 $ and a vertically descending flow just below the source for $ \ delta t < 0 $. the maximum flow velocities always occur within the ascending / descending plumes. the sph predictions are found to match the experimental observations acceptably well with root - mean - square errors in the velocity profiles of the order of $ \ sim 10 ^ { - 5 } $ m s $ ^ { - 1 } $. the fact that the sph method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach. | arxiv:2012.06055 |
the outward - pointing principal null direction of the schwarzschild riemann tensor is null hypersurface - forming. if the schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history of an outgoing light - like shell. the outward - - pointing principal null direction of the kerr riemann tensor is asymptotically ( in the neighbourhood of future null infinity ) null hypersurface - forming. if the kerr parameters of mass and angular momentum spontaneously jump across one such asymptotic hypersurface then the asymptotic hypersurface is shown to be the history of an outgoing light - like shell and a wire singularity - free spherical impulsive gravitational wave. | arxiv:gr-qc/9705042 |
capsule networks are a recently developed class of neural networks that potentially address some of the deficiencies with traditional convolutional neural networks. by replacing the standard scalar activations with vectors, and by connecting the artificial neurons in a new way, capsule networks aim to be the next great development for computer vision applications. however, in order to determine whether these networks truly operate differently than traditional networks, one must look at the differences in the capsule features. to this end, we perform several analyses with the purpose of elucidating capsule features and determining whether they perform as described in the initial publication. first, we perform a deep visualization analysis to visually compare capsule features and convolutional neural network features. then, we look at the ability for capsule features to encode information across the vector components and address what changes in the capsule architecture provides the most benefit. finally, we look at how well the capsule features are able to encode instantiation parameters of class objects via visual transformations. | arxiv:2001.10964 |
we investigate the solution of the equation \ partial _ t e ( x, t ) - id \ partial _ x ^ 2 e ( x, t ) = \ lambda | s ( x, t ) | ^ 2 e ( x, t ) $, for x in a circle and s ( x, t ) a gaussian stochastic field with a covariance of a particular form. it is shown that the coupling \ lambda _ c at which < | e | > diverges for t > = 1 ( in suitable units ), is always less or equal for d > 0 than d = 0. | arxiv:math-ph/0403018 |
this paper presents a new multi - view rgb - d dataset of nine kitchen scenes, each containing several objects in realistic cluttered environments including a subset of objects from the bigbird dataset. the viewpoints of the scenes are densely sampled and objects in the scenes are annotated with bounding boxes and in the 3d point cloud. also, an approach for detection and recognition is presented, which is comprised of two parts : i ) a new multi - view 3d proposal generation method and ii ) the development of several recognition baselines using alexnet to score our proposals, which is trained either on crops of the dataset or on synthetically composited training images. finally, we compare the performance of the object proposals and a detection baseline to the washington rgb - d scenes ( wrgb - d ) dataset and demonstrate that our kitchen scenes dataset is more challenging for object detection and recognition. the dataset is available at : http : / / cs. gmu. edu / ~ robot / gmu - kitchens. html. | arxiv:1609.07826 |
numerical simulations of the evolution of strange - mode instabilities into the non - linear regime have been performed for a wide range of stellar parameters for wolf - rayet stars. it has been shown that the wolf - rayet models reach radial velocities which amount to up to 30 % of their escape velocity. the acoustic luminosities suggest a connection to the observed mass loss. most of the models show a jump in the mean effective temperature after reaching the non - linear regime. this jump is related to the run of the opacity. | arxiv:0908.1029 |
predator - prey networks originating from different aqueous and terrestrial environments are compared to assess if the difference in environments of these networks produce any significant difference in the structure of such predator - prey networks. spectral graph theory is used firstly to discriminate between the structure of such predator - prey networks originating from aqueous and terrestrial environments and secondly to establish that the difference observed in the structure of networks originating from these two environments are precisely due to the way edges are oriented in these networks and are not a property of random networks. we use random projections in $ \ mathbb { r ^ 2 } $ and $ \ mathbb { r ^ 3 } $ of weighted spectral distribution ( wsd ) of the networks belonging to the two classes viz. aqueous and terrestrial to differentiate between the structure of these networks. the spectral theory of graph non - randomness and relative non - randomness is used to establish the deviation of structure of these networks from having a topology similar to random networks. we thus establish the absence of a universal structural pattern across predator - prey networks originating from different environments. | arxiv:1901.02883 |
perovskite nickelate heterostructure consisting of single unit cell of eunio $ _ 3 $ and lanio $ _ 3 $ have been grown on a set of single crystalline substrates by pulsed laser interval deposition to investigate the effect of epitaxial strain on electronic and magnetic properties at the extreme interface limit. despite the variation of substrate in - plane lattice constants and lattice symmetry, the structural response to heterostructuring is primarily controlled by the presence of eunio $ _ 3 $ layer. in sharp contrast to bulk lanio $ _ 3 $ or eunio $ _ 3 $, the superlattices grown under tensile strains exhibit metal to insulator transition ( mit ) below room temperature. the onset of magnetic and electronic transitions associated with the mit can be further separated by application of large tensile strain. furthermore, these transitions can be entirely suppressed by very small compressive strain. x - ray resonant absorption spectroscopy measurements reveal that such strain - controlled mit is directly linked to strain induced self - doping effect without any chemical doping. | arxiv:1807.00449 |
neural signed distance functions ( sdfs ) are emerging as an effective representation for 3d shapes. state - of - the - art methods typically encode the sdf with a large, fixed - size neural network to approximate complex shapes with implicit surfaces. rendering with these large networks is, however, computationally expensive since it requires many forward passes through the network for every pixel, making these representations impractical for real - time graphics. we introduce an efficient neural representation that, for the first time, enables real - time rendering of high - fidelity neural sdfs, while achieving state - of - the - art geometry reconstruction quality. we represent implicit surfaces using an octree - based feature volume which adaptively fits shapes with multiple discrete levels of detail ( lods ), and enables continuous lod with sdf interpolation. we further develop an efficient algorithm to directly render our novel neural sdf representation in real - time by querying only the necessary lods with sparse octree traversal. we show that our representation is 2 - 3 orders of magnitude more efficient in terms of rendering speed compared to previous works. furthermore, it produces state - of - the - art reconstruction quality for complex shapes under both 3d geometric and 2d image - space metrics. | arxiv:2101.10994 |
efficient methods to determine the relative position of two conics are of great interest for applications in robotics, computer animation, cagd, computational physics, and other areas. we present a method to obtain the relative position of a parabola or a hyperbola, and a coplanar ellipse, directly from the coefficients of their implicit equations, even if they are not given in canonical form, and avoiding the computation of the corresponding intersection points ( and their characteristics ). | arxiv:2505.00706 |
recommendation algorithms are susceptible to popularity bias : a tendency to recommend popular items even when they fail to meet user needs. a related issue is that the recommendation quality can vary by demographic groups. marginalized groups or groups that are under - represented in the training data may receive less relevant recommendations from these algorithms compared to others. in a recent study, ekstrand et al. investigate how recommender performance varies according to popularity and demographics, and find statistically significant differences in recommendation utility between binary genders on two datasets, and significant effects based on age on one dataset. here we reproduce those results and extend them with additional analyses. we find statistically significant differences in recommender performance by both age and gender. we observe that recommendation utility steadily degrades for older users, and is lower for women than men. we also find that the utility is higher for users from countries with more representation in the dataset. in addition, we find that total usage and the popularity of consumed content are strong predictors of recommender performance and also vary significantly across demographic groups. | arxiv:2110.08353 |
we construct extended tqfts associated to rozansky - - witten models with target manifolds $ t ^ * \ mathbb { c } ^ n $. the starting point of the construction is the 3 - category whose objects are such rozansky - - witten models, and whose morphisms are defects of all codimensions. by truncation, we obtain a ( non - semisimple ) 2 - category $ \ mathcal { c } $ of bulk theories, surface defects, and isomorphism classes of line defects. through a systematic application of the cobordism hypothesis we construct a unique extended oriented 2 - dimensional tqft valued in $ \ mathcal { c } $ for every affine rozansky - - witten model. by evaluating this tqft on closed surfaces we obtain the infinite - dimensional state spaces ( graded by flavour and r - charges ) of the initial 3 - dimensional theory. furthermore, we explicitly compute the commutative frobenius algebras that classify the restrictions of the extended theories to circles and bordisms between them. | arxiv:2201.03284 |
we analyze quantum entanglement of stokes light and atomic electronic polarization excited during single - pass, linear - regime, stimulated raman scattering in terms of optical wave - packet modes and atomic - ensemble spatial modes. the output of this process is confirmed to be decomposable into multiple discrete, bosonic mode pairs, each pair undergoing independent evolution into a two - mode squeezed state. for this we extend the bloch - messiah reduction theorem, previously known for discrete linear systems ( s. l. braunstein, phys. rev. a, vol. 71, 055801 ( 2005 ) ). we present typical mode functions in the case of one - dimensional scattering in an atomic vapor. we find that in the absence of dispersion, one mode pair dominates the process, leading to a simple interpretation of entanglement in this continuous - variable system. however, many mode pairs are excited in the presence of dispersion - induced temporal walkoff of the stokes, as witnessed by the photon - count statistics. we also consider the readout of the stored atomic polarization using the anti - stokes scattering process. we prove that the readout process can also be decomposed into multiple mode pairs, each pair undergoing independent evolution analogous to a beam - splitter transformation. we show that this process can have unit efficiency under realistic experimental conditions. the shape of the output light wave packet can be predicted. in case of unit readout efficiency it contains only excitations originating from a specified atomic excitation mode. | arxiv:quant-ph/0512157 |
quantum error correction is crucial for universal fault - tolerant quantum computing. highly accurate and low - time - complexity decoding algorithms play an indispensable role in ensuring quantum error correction works effectively. among existing decoding algorithms, belief propagation ( bp ) is notable for its nearly linear time complexity and general applicability to stabilizer codes. however, bp ' s decoding accuracy without post - processing is unsatisfactory in most situations. this article focuses on improving the decoding accuracy of bp over gf ( 4 ) for surface codes. inspired by machine learning optimization techniques, we first propose momentum - bp and adagrad - bp to reduce oscillations in message updating, breaking the trapping sets of surface codes. we further propose ewainit - bp, which adaptively updates initial probabilities and provides a 1 to 3 orders of magnitude improvement over traditional bp for planar surface code, toric code, and xzzx surface code without any post - processing method, showing high decoding accuracy even under parallel scheduling. the theoretical $ o ( 1 ) $ time complexity under parallel implementation and high accuracy of ewainit - bp make it a promising candidate for high - precision real - time decoders. | arxiv:2407.11523 |
in robbins ' problem of minimizing the expected rank, a finite sequence of $ n $ independent, identically distributed random variables are observed sequentially and the objective is to stop at such a time that the expected rank of the selected variable ( among the sequence of all $ n $ variables ) is as small as possible. in this paper we consider an analogous problem in which the observed random variables are the steps of a symmetric random walk. assuming continuously distributed step sizes, we describe the optimal stopping rules for the cases $ n = 2 $ and $ n = 3 $ in two versions of the problem : a " full information " version in which the actual steps of the random walk are disclosed to the decision maker ; and a " partial information " version in which only the relative ranks of the positions taken by the random walk are observed. when $ n = 3 $, the optimal rule and expected rank depend on the distribution of the step sizes. we give sharp bounds for the optimal expected rank in the partial information version, and fairly sharp bounds in the full information version. | arxiv:1811.07096 |
in this paper, we consider a three node relay network comprising a source, a relay, and a destination. the source transmits the message to the destination using hybrid automatic repeat request ( harq ) with incremental redundancy ( ir ). the relay overhears the transmitted message, amplifies it using a variable gain amplifier, and then forwards the message to the destination. this latter combines both the source and the relay message and tries to decode the information. in case of decoding failure, the destination sends a negative acknowledgement. a new replica of the message containing new parity bits is then transmitted in the subsequent harq round. this process continues until successful decoding occurs at the destination or a maximum number $ m $ of rounds is reached. we study the performance of harq - ir over the considered relay channel from an information theoretic perspective. we derive exact expressions and bounds for the information outage probability, the average number of transmissions, and the average transmission rate. moreover, we evaluate the delay experienced by poisson arriving packets over the considered relay network. we also provide analytical expressions for the expected waiting time, the sojourn time, and the energy efficiency. the derived exact expressions are validated by monte carlo simulations. | arxiv:1404.2131 |
fermi problems ( fps ) are mathematical reasoning tasks that require human - like logic and numerical reasoning. unlike other reasoning questions, fps often involve real - world impracticalities or ambiguous concepts, making them challenging even for humans to solve. despite advancements in ai, particularly with large language models ( llms ) in various reasoning tasks, fps remain relatively under - explored. this work conducted an exploratory study to examine the capabilities and limitations of llms in solving fps. we first evaluated the overall performance of three advanced llms using a publicly available fp dataset. we designed prompts according to the recently proposed teler taxonomy, including a zero - shot scenario. results indicated that all three llms achieved a fp _ score ( range between 0 - 1 ) below 0. 5, underscoring the inherent difficulty of these reasoning tasks. to further investigate, we categorized fps into standard and specific questions, hypothesizing that llms would perform better on standard questions, which are characterized by clarity and conciseness, than on specific ones. comparative experiments confirmed this hypothesis, demonstrating that llms performed better on standard fps in terms of both accuracy and efficiency. | arxiv:2504.02671 |
solar active region ( ar ) 12673 produced 4 x - class, 27 m - class, and numerous lower class flares during its passage across the visible solar disk in september 2017. our study is to answer the questions why this ar was so flare - productive and how the x9. 3 flare, the largest one of the last decade, took place. we find that there was a sunspot in the initial several days, and then two bipolar regions emerged nearby it successively. due to the standing of the pre - existing sunspot, the movement of the bipoles was blocked, while the pre - existing sunspot maintained its quasi - circular shaped umbra only with the disappearance of a part of penumbra. thus, the bipolar patches were significantly distorted, and the opposite polarities formed two semi - circular shaped structures. after that, two sequences of new bipolar regions emerged within the narrow semi - circular zone, and the bipolar patches separated along the curved channel. the new bipoles sheared and interacted with the previous ones, forming a complex topological system, during which numerous flares occurred. at the highly sheared region, a great deal of free energy was accumulated. on september 6, one negative patch near the polarity inversion line began to rapidly rotate and shear with the surrounding positive fields, and consequently the x9. 3 flare erupted. our results reveal that the block - induced complex structures built the flare - productive ar and the x9. 3 flare was triggered by an erupting filament due to the kink instability. to better illustrate this process, a block - induced eruption model is proposed for the first time. | arxiv:1710.06545 |
an exponential luenberger dynamical observer is proposed to estimate the state of a general class of nonautonomous semilinear parabolic equations. the result can be applied to the case where the output is given by state measurements taken at a finite number of spatial points, that is, to the case where our sensors are a finite number of delta distributions. the output injection operator is explicit and the derivation of the main result involves the decomposition of the state space into a direct sum of two oblique components depending on the set of sensors. simulations are presented as an application to the kuramoto - - sivashinsky models for flame propagation and fluid flow. | arxiv:2212.01879 |
we prove exponential convergence to equilibrium for the fredrikson - andersen one spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. this was a classical conjecture related to non - attractive spin systems. our proof rely on coupling techniques based on harris graphical construction for interacting particle systems. | arxiv:1609.01364 |
we study private stochastic convex optimization ( sco ) under user - level differential privacy ( dp ) constraints. in this setting, there are $ n $ users ( e. g., cell phones ), each possessing $ m $ data items ( e. g., text messages ), and we need to protect the privacy of each user ' s entire collection of data items. existing algorithms for user - level dp sco are impractical in many large - scale machine learning scenarios because : ( i ) they make restrictive assumptions on the smoothness parameter of the loss function and require the number of users to grow polynomially with the dimension of the parameter space ; or ( ii ) they are prohibitively slow, requiring at least $ ( mn ) ^ { 3 / 2 } $ gradient computations for smooth losses and $ ( mn ) ^ 3 $ computations for non - smooth losses. to address these limitations, we provide novel user - level dp algorithms with state - of - the - art excess risk and runtime guarantees, without stringent assumptions. first, we develop a linear - time algorithm with state - of - the - art excess risk ( for a non - trivial linear - time algorithm ) under a mild smoothness assumption. our second algorithm applies to arbitrary smooth losses and achieves optimal excess risk in $ \ approx ( mn ) ^ { 9 / 8 } $ gradient computations. third, for non - smooth loss functions, we obtain optimal excess risk in $ n ^ { 11 / 8 } m ^ { 5 / 4 } $ gradient computations. moreover, our algorithms do not require the number of users to grow polynomially with the dimension. | arxiv:2410.18391 |
potential strength of the cosmic chronometers approach up to $ z > 1 $, especially in view of incoming large spectroscopic surveys like euclid. ( abridged ) | arxiv:2305.16387 |
the parametrization theorem is derived in a flat nd pseudo - complex affine space. the pseudo - complex hyperbolic space accomodates n - number of uncompactified time - like extra dimensions with sugnature ( s, r ), where s and r are the numbers of minus and plus signs associated with the diagonalized metric matrix. the main result of the theorem suggests a uniform parametrization for both time - like and space - like dimensions. the uniformization requirement preserves complex - hyperbolic inner product associated with the space. as application, the elements of the space is shown to be invariant under linear transformation. | arxiv:1003.0422 |
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