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by regular tessellation, we mean any hyperbolic 3 - manifold tessellated by ideal platonic solids such that the symmetry group acts transitively on oriented flags. a regular tessellation has an invariant we call the cusp modulus. for small cusp modulus, we classify all regular tessellations. for large cusp modulus, we prove that a regular tessellations has to be infinite volume if its fundamental group is generated by peripheral curves only. this shows that there are at least 19 and at most 21 link complements that are regular tessellations ( computer experiments suggest that at least one of the two remaining cases likely fails to be a link complement, but so far we have no proof ). in particular, we complete the classification of all principal congruence link complements given in baker and reid for the cases of discriminant d = - 3 and d = - 4. we only describe the manifolds arising as complements of links here with a future publication " regular tessellation links " giving explicit pictures of these links. | arxiv:1406.2827 |
magnetic field fluctuations in the vicinity of the earth ' s bow shock have been investigated with the aim to characterize the intermittent behaviour of strong plasma turbulence. the observed small - scale intermittency may be the signature of a multifractal process but a deeper inspection reveals caveats in such an interpretation. several effects, including the anisotropy of the wavefield, the violation of the taylor hypothesis and the occasional occurrence of coherent wave packets, strongly affect the higher order statistical properties. after correcting these effects, a more gaussian and scale - invariant wavefield is recovered. | arxiv:comp-gas/9607003 |
this paper considers how to ensure that a system of fixed wing unmanned aerial vehicles ( uavs ) can avoid collisions. to do so we develop a novel method for creating a barrier function, which is similar to a lyapunov function and can be used to ensure that a system can stay safe for all future times. after introducing the general approach, it is shown how to ensure that collision avoidance for two vehicles can be guaranteed for all future times. the construction is then extended to the case of arbitrarily many vehicles by addressing how to satisfy multiple safety objectives simultaneously. we do this while ensuring output actuator commands are within specified limits. because this formulation requires communication of control values and may therefore reduce throughput of other important messages, we then show how to reformulate the solution without this significant communication overhead while still ensuring safety is maintained and actuator limits are respected. we validate the theoretical developments of this paper in the simulator scrimmage with a simulation of 20 uavs that maintain safe distances from each other even though their nominal paths would otherwise cause a collision. | arxiv:1906.03771 |
the antifield - brst formalism and the various cohomologies associated with it are surveyed and illustrated in the context of yang - mills gauge theory. in particular, the central role played by the koszul - tate resolution and its relation to the characteristic cohomology are stressed. | arxiv:hep-th/9412141 |
microwave transversal filters, which are implemented based on the transversal filter structure in digital signal processing, offer a high reconfigurability for achieving a variety of signal processing functions without changing hardware. when implemented using microwave photonic ( mwp ) technologies, also known as mwp transversal filters, they provide competitive advantages over their electrical counterparts, such as low loss, large operation bandwidth, and strong immunity to electromagnetic interference. recent advances in high performance optical microcombs provide compact and powerful multiwavelength sources for mwp transversal filters that require a larger number of wavelength channels to achieve high performance, allowing for the demonstration of a diverse range of filter functions with improved performance and new features. here, we present a comprehensive performance analysis for microcomb based mwp spectral filters based on the transversal filter approach. first, we investigate the theoretical limitations in the filter spectral response induced by finite tap numbers. next, we analyze the distortions in the filter spectral response resulting from experimental error sources. finally, we assess the influence of input signals bandwidth on the filtering errors. these results provide a valuable guide for the design and optimization of microcomb - based mwp transversal filters for a variety of applications. | arxiv:2408.03547 |
beta = 1. 3 + / - 0. 2, in agreement with the values obtained above. | arxiv:1011.0725 |
boron ( b ) sheet has been intently studied and various candidates with vacancies have been proposed by theoretical investigations, including the possible growth on metal surface. however, a recent experiment ( science 350, 1513, 2015 ) reported that the sheet formed on the ag ( 111 ) surface was a buckled triangular lattice without vacancy. our calculations combined with high - throughput screening and the first - principles method demonstrate a novel growth mechanism of boron sheet from clusters, ribbons, to monolayers, where the b - ag interaction is dominant in the nucleation of boron nanostructures. we have found that the simulated stm image of the sheet with 1 / 6 vacancies in a stripe pattern is in better agreement with the experimental observation, which is energetically favored during the nucleation and growth. | arxiv:1601.01393 |
covert communication can prevent the adversary from knowing that a wireless transmission has occurred. in the additive white gaussian noise channels, a square root law is obtained and the result shows that alice can reliably and covertly transmit $ \ mathcal { o } ( \ sqrt { n } ) $ bits to bob in $ n $ channel uses. if additional " friendly " node near the adversary can inject artificial noise to aid alice in hiding her transmission attempt, covert throughput can be improved, i. e., alice can covertly transmit $ \ mathcal { o } ( \ min \ { n, \ lambda ^ { \ alpha / 2 } \ sqrt { n } \ } ) $ bits to bob over $ n $ uses of the channel ( $ \ lambda $ is the density of friendly nodes and $ \ alpha $ is the path loss exponent of wireless channels ). in this paper, we consider the covert communication in a noisy wireless network, where bob and the adversary willie not only experience the background noise, but also the aggregated interference from other transmitters. our results show that uncertainty in interference experienced by willie is beneficial to alice. when the distance between alice and willie $ d _ { a, w } = \ omega ( n ^ { \ delta / 4 } ) $ ( $ \ delta = 2 / \ alpha $ is stability exponent ), alice can reliably and covertly transmit $ \ mathcal { o } ( \ log _ 2 \ sqrt { n } ) $ bits to bob in $ n $ channel uses. although the covert throughput is lower than the square root law and the friendly jamming scheme, the spatial throughput is higher. from the network perspective, the communications are hidden in " the sound and the fury " of noisy wireless networks, and what willie sees is merely a " shadow " wireless network. he knows for certain that some nodes are transmitting, but he cannot catch anyone red - handed. | arxiv:1712.05099 |
a new measurement of the 1s - 2s energy splitting of muonium by doppler - free two - photon spectroscopy has been performed at the rutherford appleton laboratory in chilton, didcot, uk. increased accuracy is expected compared to a previous experiment. spectroscopy of this transistion promises an improvement of the muon mass value. | arxiv:physics/9805020 |
we study almost bi - paracontact structures on contact manifolds. we prove that if an almost bi - paracontact structure is defined on a contact manifold $ ( m, \ eta ) $, then under some natural assumptions of integrability, $ m $ carries two transverse bi - legendrian structures. conversely, if two transverse bi - legendrian structures are defined on a contact manifold, then $ m $ admits an almost bi - paracontact structure. we define a canonical connection on an almost bi - paracontact manifold and we study its curvature properties, which resemble those of the obata connection of an anti - hypercomplex ( or complex - product ) manifold. further, we prove that any contact metric manifold whose reeb vector field belongs to the $ ( \ kappa, \ mu ) $ - nullity distribution canonically carries an almost bi - paracontact structure and we apply the previous results to the theory of contact metric $ ( \ kappa, \ mu ) $ - spaces. | arxiv:1003.1417 |
this paper considers the transmission of an infinite sequence of messages ( a streaming source ) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. while the capacity of a channel that introduces only bursts of erasures is well known, only recently, the capacity of a channel with either one burst of erasures or multiple arbitrary erasures in any fixed - sized sliding window has been established. however, the codes shown to achieve this capacity are either non - explicit constructions ( proven to exist ) or explicit constructions that require large field size that scales exponentially with the delay. this work describes an explicit rate - optimal construction for admissible channel and delay parameters over a field size that scales only quadratically with the delay. | arxiv:1904.06212 |
mathematical method based on a direct or indirect analysis of growth rates is described. it is shown how simple assumptions and a relatively easy analysis can be used to describe mathematically complicated trends and to predict growth. only rudimentary knowledge of calculus is required. projected trajectories based on such simple initial assumptions are easier to accept and to understand than alternative complicated projections based on more complicated assumptions and on more intricate computational procedures. examples of the growth of population and of the growth of the gross domestic product are used to illustrate the application of this method of forecasting. | arxiv:1705.06557 |
nanoclusters like fullerenes as the unit to build intriguing two - dimensional topological structures is of great challenge. here we propose three bridged fullerene monolayers and comprehensively investigate the novel fullerene monolayer as synthesized experimentally zheng et al., [ nature 606, 507 - 510 ( 2022 ) ] by state of the art first principles calculations. our results show that alpha - c60 - 2d has a direct bandgap of 1. 49 ev owing to a flat conduction band bottom close to the experimental value, the optical linear dichroism with strong absorption in long - wave ultraviolet region, a small anisotropic youngs modulus, the large hole mobility, and the ultrahigh seebeck coefficient at middle low temperatures. moreover, li ions are found to migrate easily along the x path in alpha - c60 - 2d. it is unveiled that the anisotropic optical, mechanical, electrical, and thermoelectric properties of alpha - c60 - 2d originate from the asymmetric bridging arrangements between c60 clusters. our study promises potential applications of monolayer fullerene networks in diverse fields. | arxiv:2207.02781 |
in this paper i generalize the halo model for the clustering of dark matter in order to produce the power spectra of the two main baryonic matter components in the universe : stars and hot gas. as a natural extension, this can be also used to describe the clustering of all mass. according to the design of the halo model, the large - scale power spectra of the various matter components are physically connected with the distribution of each component within bound structures and thus, ultimately, with the complete set of physical processes that drive the formation of galaxies and galaxy clusters. besides being practical for cosmological and parametric studies, the semi - analytic model presented here has also other advantages. most importantly, it allows one to understand on physical ground what is the relative contribution of each matter component to the total clustering of mass as a function of scale, and thus it opens an interesting new window to infer the distribution of baryons through high precision cosmic shear measurements. this is particularly relevant for future wide - field photometric surveys such as euclid. in this work the concept of the model and its uncertainties are illustrated in detail, while in a companion paper we use a set of numerical hydrodynamic simulations to show a practical application and to investigate where the model itself needs to be improved. | arxiv:1401.2997 |
developing the analysis of the distribution of the particle ' s position - momentum dot product, the so - called \ textit { posmom } $ \ mathbf { x } % \ cdot \ mathbf { p } $ \ textbf {, } to quantum states on a circular circle on two - dimensional cartesian coordinates, we give its posmometry ( introduced recently by y. a. bernard and p. m. w. gill, posmom : the unobserved observable, j. phys. chem. lett. 1 \ textbf { ( } 2010 \ textbf { ) } 1254 ) for eigenstates of the free motion on the circle, i. e., $ z $ - axis component of the angular momentum. the posmom has two parity symmetries, specifically, invariant under two operations $ m _ { x } $ and $ m _ { y } $ representing mirror symmetry about $ x $ and $ y $ axis respectively. the complete eigenfunction set of the posmom is then four - valued and consists of four basic parts each of them is defined within a distinct quadrant of the circle. the results are not only potentially experimentally testable, but also reflect a fact that the embedding of the circle $ s ^ { 1 } $ in two - dimensional flat space $ r ^ { 2 } $ is physically reasonable. | arxiv:1410.1010 |
we obtain a limit theorem endowed with quantitative estimates for a general class of infinite dimensional hybrid processes with intrinsically two different time scales and including a population. as an application, we consider a large class of conductance - based neuron models describing the nerve impulse propagation along a neural cell at the scales of ion channels. | arxiv:1403.1751 |
true random number generators ( trngs ) are essential components of cryptographic designs, which are used to generate private keys for encryption and authentication, and are used in masking countermeasures. in this work, we present a mechanism to design a stealthy parametric hardware trojan for a ring oscillator based trng architecture proposed by yang et al. at isscc 2014. once the trojan is triggered the malicious trng generates predictable non - random outputs. such a trojan does not require any additional logic ( even a single gate ) and is purely based on subtle manipulations on the sub - transistor level. the underlying concept is to disable the entropy source at high temperature to trigger the trojan, while ensuring that trojan - infected trng works correctly under normal conditions. we show how an attack can be performed with the trojan - infected trng design in which the attacker uses a stochastic markov chain model to predict its reduced - entropy outputs. | arxiv:1910.00735 |
numerous studies have proved their effective strength in detecting control area network ( can ) attacks. in the realm of understanding the human semantic space, transformer - based models have demonstrated remarkable effectiveness. leveraging pre - trained transformers has become a common strategy in various language - related tasks, enabling these models to grasp human semantics more comprehensively. to delve into the adaptability evaluation on pre - trained models for can intrusion detection, we have developed two distinct models : can - securebert and can - llama2. notably, our can - llama2 model surpasses the state - of - the - art models by achieving an exceptional performance 0. 999993 in terms of balanced accuracy, precision detection rate, f1 score, and a remarkably low false alarm rate of 3. 10e - 6. impressively, the false alarm rate is 52 times smaller than that of the leading model, mth - ids ( multitiered hybrid intrusion detection system ). our study underscores the promise of employing a large language model as the foundational model, while incorporating adapters for other cybersecurity - related tasks and maintaining the model ' s inherent language - related capabilities. | arxiv:2311.12074 |
we study an isotropic flat flrw - model in scale - covariant theory of gravity $ f _ { \ gamma \ delta } ( \ phi ) $ \ cite { canuto : 1977zz } which is explained in terms of ordinary and covariant differentiation of scalar field $ \ phi $. as we know the deceleration parameter is time - dependent, so we consider the deceleration parameter $ q $ as the function of $ t $. using this methodology, we find all the important cosmological factors in terms of a hyperbolic function of the cosmic time $ t $. in turn, we create the model having the behavior of the late - time universe, which is ever accelerated expanding and faces a big freeze at the end. the model shows the quintessence dark energy model from early to late times. we compute the constrained values of hubble parameter $ h _ 0 = 70. 979 ^ { + 0. 021 } _ { - 0. 0043 } $ and the model parameter $ n = 1. 24079 ^ { + 0. 00015 } _ { - 0. 00079 } $ using joint analysis of the $ ohd $ data of 77 - points and pantheon bin data. the model exhibits point - type singularity, beginning with a point of zero volume, infinite energy density, and temperature. furthermore, we obtain the present deceleration parameter $ ( q _ 0 ) \ approx { - 0. 54 } $. also, we examine the ultimate behavior of our model by properly analyzing energy conditions, cosmographical parameters, and statefinder diagnostic. finally, the proposed model behaves like a quintessence dark energy model. | arxiv:2207.05076 |
in this communication we analyze the behavior of excited drops contained in spherical volumes. we study different properties of the dynamical systems i. e. the maximum lyapunov exponent mle, the asymptotic distance in momentum space $ d _ { \ infty } $ andthe normalized variance of the maximum fragment nvm. it is shown that the constrained systems behaves as undergoing a first order phase transition at low densities while as a second order one at high densities. the transition from liquid - like to vapor - like behavior is signaled both by the caloric curves, thermal response functions and the mle. the relationship between $ mle, d _ { \ infty } $, and the cc is explored. | arxiv:nucl-th/0203049 |
we reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. a slight modification of depth - first search leads to an algorithm for finding such paths. although this setting is equivalent to the traditional terminology of blossoms due to edmonds, there are some advantages. mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. exemplary, we describe an efficient realization of the hopcroft - karp approach for the computation of a maximum cardinality matching in general graphs and a variant of edmonds ' primal - dual algorithm for the maximum weighted matching problem. | arxiv:1509.04927 |
we present a method for the controlled and robust generation of spatial superposition states of single atoms in micro - traps. using a counter - intuitive positioning sequence for the individual potentials and appropriately chosen trapping frequencies, we show that it is possible to selectively create two different orthogonal superposition states, which can in turn be used for quantum information purposes. | arxiv:quant-ph/0611174 |
one attractive approach to market dynamics is the level $ k $ model in which a level $ 0 $ player adopts a very simple response to current conditions, a level $ 1 $ player best - responds to a model in which others take level $ 0 $ actions, and so forth. ( this is analogous to $ k $ - ply exploration of game trees in ai, and to receding - horizon control in control theory. ) if players have deterministic mental models with this kind of finite - level response, there is obviously no way their mental models can all be consistent. nevertheless, there is experimental evidence that people act this way in many situations, motivating the question of what the dynamics of such interactions lead to. we address this question in the setting of fisher markets with constant elasticities of substitution ( ces ) utilities, in the weak gross substitutes ( wgs ) regime. we show that despite the inconsistency of the mental models, and even if players ' models change arbitrarily from round to round, the market converges to its unique equilibrium. ( we show this for both synchronous and asynchronous discrete - time updates. ) moreover, the result is computationally feasible in the sense that the convergence rate is linear, i. e., the distance to equilibrium decays exponentially fast. to the best of our knowledge, this is the first result that demonstrates, in fisher markets, convergence at any rate for dynamics driven by a plausible model of seller incentives. even for the simple case of ( level $ 0 $ ) best - response dynamics, where we observe that convergence at some rate can be derived from recent results in convex optimization, our result is the first to demonstrate a linear rate of convergence. | arxiv:1605.09012 |
shear - free or asymptotically shear - free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. it is the purpose of this paper to develop these issues and find applications in gr. the applications center around the problem of extracting interior physical properties of an asymptotically flat space - time directly from the asymptotic gravitational ( and maxwell ) field itself in analogy with the determination of total charge by an integral over the maxwell field at infinity or the identification of the interior mass ( and its loss ) by ( bondi ' s ) integrals of the weyl tensor, also at infinity. more specifically we will see that the asymptotically shear - free congruences lead us to an asymptotic definition of the center - of - mass and its equations of motion. this includes a kinematic meaning, in terms of the center of mass motion, for the bondi three - momentum. in addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well - defined flux terms. when a maxwell field is present the asymptotically shear - free congruences allow us to determine / define at infinity a center - of - charge world - line and intrinsic magnetic dipole moment. | arxiv:0906.2155 |
the transformer model has revolutionized natural language processing tasks such as neural machine translation, and many efforts have been made to study the transformer architecture, which increased its efficiency and accuracy. one potential area for improvement is to address the computation of empty tokens that the transformer computes only to discard them later, leading to an unnecessary computational burden. to tackle this, we propose an algorithm that sorts translation sentence pairs based on their length before batching, minimizing the waste of computing power. since the amount of sorting could violate the independent and identically distributed ( i. i. d ) data assumption, we sort the data partially. in experiments, we apply the proposed method to english - korean and english - luganda language pairs for machine translation and show that there are gains in computational time while maintaining the performance. our method is independent of architectures, so that it can be easily integrated into any training process with flexible data lengths. | arxiv:2308.08153 |
the solution representing a brane - anti - brane system in matrix models breaks the usual matrix spacetime symmetry. we show that the spacetime symmetry on the branes is not breaking, rather appears as a combination of the matrix spacetime transformation and a gauge transformation. as a result, the tachyon field, itself an off - diagonal entry in longitudinal matrices, transforms nontrivially under rotations, decomposing into tensors of different ranks. we also show that the tachyon field can never be gauged away, and conjecture that this field is related to the usual complex scalar tachyon by a field redefinition. we also briefly discuss tachyon condensation. | arxiv:hep-th/0010058 |
diffusion models have been extensively utilized in ai - generated content ( aigc ) in recent years, thanks to the superior generation capabilities. combining with semantic communications, diffusion models are used for tasks such as denoising, data reconstruction, and content generation. however, existing diffusion - based generative models do not consider the stringent bandwidth limitation, which limits its application in wireless communication. this paper introduces a diffusion - driven semantic communication framework with advanced vae - based compression for bandwidth - constrained generative model. our designed architecture utilizes the diffusion model, where the signal transmission process through the wireless channel acts as the forward process in diffusion. to reduce bandwidth requirements, we incorporate a downsampling module and a paired upsampling module based on a variational auto - encoder with reparameterization at the receiver to ensure that the recovered features conform to the gaussian distribution. furthermore, we derive the loss function for our proposed system and evaluate its performance through comprehensive experiments. our experimental results demonstrate significant improvements in pixel - level metrics such as peak signal to noise ratio ( psnr ) and semantic metrics like learned perceptual image patch similarity ( lpips ). these enhancements are more profound regarding the compression rates and snr compared to deep joint source - channel coding ( djscc ). | arxiv:2407.18468 |
we present an example of a zero - dimensional compact metric space $ x $ and its closed subspace $ a $ such that there is no continuous linear extension operator for the lipschitz pseudometrics on $ a $ to the lipschitz pseudometrics on $ x $. the construction is based on results of a. brudnyi and yu. brudnyi concerning linear extension operators for lipschitz functions. | arxiv:1207.2952 |
a number of numerical simulations of lattice gauge theory have indicated a low mass of strange quark in 100 mev range at the scale of $ \ mu = 2 $ gev. in the unquenched case, which is improved over the simulation in the quenched approximation by the inclusion of $ u $ and $ d $ sea quark effects, one sees a further downward trend. here the fermion mass spectrum of the fritzsch texture is recalculated. in a single step supersymmetric gut with $ m _ x \ sim 10 ^ { 16 } $ gev such values of the strange quark mass can be obtained for low values of $ \ tan \ beta $. experimental numbers $ m ^ { pole } _ t = 173 \ pm 6 $ gev and $ 4. 1 < m _ b ( m _ b ) < 4. 4 $ gev are used in this study. since the scenario is supersymmetric, gaugino loop diagrams contribute to the masses in addition to usual tree level yukawa contributions. upper bound of the mixing parameter $ v _ { cb } $ is taken at 0. 045 | arxiv:hep-ph/0001060 |
the proximity effect of superconductivity on confined states in semiconductors gives rise to various bound states such as andreev bound states ( abss ), andreev molecules and majorana zero modes. while such bound states do not conserve charge, their fermion parity is a good quantum number. one way to measure parity is to convert it to charge first, which is then sensed. in this work, we sense the charge of abss and andreev molecules in an insb - al hybrid nanowire using an integrated quantum dot operated as a charge sensor. we show how charge sensing measurements can resolve the even and odd states of an andreev molecule, without affecting the parity. such an approach can be further utilized for parity measurements of majorana zero modes in kitaev chains based on quantum dots. | arxiv:2311.02001 |
quantum parity conservation is verified at all orders in perturbation theory for a massless parity - even $ u ( 1 ) \ times u ( 1 ) $ planar quantum electrodynamics ( qed $ _ 3 $ ) model. the presence of two massless fermions requires the lowenstein - zimmermann ( lz ) subtraction scheme, in the framework of the bogoliubov - parasiuk - hepp - zimmermann - lowenstein ( bphzl ) renormalization method, in order to subtract the infrared divergences induced by the ultraviolet subtractions at 1 - and 2 - loops, however thanks to the superrenormalizability of the model the ultraviolet divergences are bounded up to 2 - loops. finally, it is proved that the bphzl renormalization method preserves parity for the model taken into consideration, contrary to what happens to the ordinary massless parity - even $ u ( 1 ) $ qed $ _ 3 $. | arxiv:2010.03125 |
persistence modules that decompose into interval modules are important in topological data analysis because we can interpret such intervals as the lifetime of topological features in the data. we can classify the settings in which persistence modules always decompose into intervals, by a recent result of aoki, escolar and tada : these are standard single - parameter persistence, zigzag persistence, and bipath persistence. no other setting offers such guarantees. we show that a bipath persistence module can be decomposed via a closely related infinite zigzag persistence module, understood as a covering. this allows us to translate techniques of zigzag persistence, like recent advancements in its efficient computation by dey and hou, to bipath persistence. in addition, and again by the relation with the infinite zigzag, we can define an interleaving and bottleneck distance on bipath persistence. in turn, the algebraic stability of zigzag persistence implies the algebraic stability of bipath persistence. | arxiv:2501.00322 |
we prove the existence of weak solutions to an unsteady thermistor system with p - laplacian type equation for the electrostatic potential, where the electrical conductivity of the thermistor material is a monotone function of the electric field density. | arxiv:1609.01440 |
this paper proposes a general framework for structure - preserving model reduction of a secondorder network system based on graph clustering. in this approach, vertex dynamics are captured by the transfer functions from inputs to individual states, and the dissimilarities of vertices are quantified by the h2 - norms of the transfer function discrepancies. a greedy hierarchical clustering algorithm is proposed to place those vertices with similar dynamics into same clusters. then, the reduced - order model is generated by the petrov - galerkin method, where the projection is formed by the characteristic matrix of the resulting network clustering. it is shown that the simplified system preserves an interconnection structure, i. e., it can be again interpreted as a second - order system evolving over a reduced graph. furthermore, this paper generalizes the definition of network controllability gramian to second - order network systems. based on it, we develop an efficient method to compute h2 - norms and derive the approximation error between the full - order and reduced - order models. finally, the approach is illustrated by the example of a small - world network. | arxiv:1706.01751 |
let $ \ mathrm { x ( n ) } $ be ravenel ' s thom spectrum over $ \ omega \ mathrm { su } ( n ) $. we say a spectrum $ e $ has chromatic defect $ n $ if $ n $ is the smallest positive integer such that $ e \ otimes \ mathrm { x ( n ) } $ is complex orientable. we compute the chromatic defect of various examples of interest : finite spectra, the real johnson - - wilson theories $ \ mathrm { er ( n ) } $, the fixed points $ \ mathrm { eo } _ n ( g ) $ of morava $ e $ - theories with respect to a finite subgroup $ g $ of the morava stabilizer group, and the connective image of $ j $ spectrum j. having finite chromatic defect is closely related to the existence of analogues of the classical wood splitting $ \ mathrm { ko } \ otimes c ( \ eta ) \ simeq \ mathrm { ku } $. we show that such splittings exist in quite a wide generality for fp spectra $ e $. when $ e $ participates in such a splitting, $ e $ admits a $ \ mathbb z $ - indexed adams - - novikov tower, which may be used to deduce differentials in the adams - - novikov spectral sequence of $ e $. | arxiv:2402.17519 |
there are steady advances in the calculation of electroweak corrections to massive scattering problems at colliders, from the very beginning in the nineteen seventies until contemporary developments. recent years brought a remarkable progress due to new calculational technologies. this was motivated by demands from phenomenological applications at particle accelerators : higher multiplicities of the final states, extreme kinematics, need of higher precision and thus of higher orders in perturbation theory. we describe selected contributions from the project " massive particle production " of sonderforschungsbereich / transregio 9 of deutsche forschungsgemeinschaft. | arxiv:1412.3311 |
z, ( z ∈ x z ∈ z ), { \ displaystyle \ forall z, ( z \ in x \ iff z \ in z ), } thus x = z. { \ displaystyle x = z. } substitution : see substitution ( logic ) § proof of substitution in zfc. function application : given a = b { \ displaystyle a = b } and f ( a ) = c, { \ displaystyle f ( a ) = c, } then ( a, c ) ∈ f. { \ displaystyle ( a, c ) \ in f. } since a = b { \ displaystyle a = b } and c = c, { \ displaystyle c = c, } then ( a, c ) = ( b, c ). { \ displaystyle ( a, c ) = ( b, c ). } this is the defining property of an ordered pair. since ( a, c ) = ( b, c ), { \ displaystyle ( a, c ) = ( b, c ), } by the axiom of extensionality, they must belong to the same sets, so, since ( a, c ) ∈ f, { \ displaystyle ( a, c ) \ in f, } we have ( b, c ) ∈ f, { \ displaystyle ( b, c ) \ in f, } or f ( b ) = c. { \ displaystyle f ( b ) = c. } thus f ( a ) = f ( b ). { \ displaystyle f ( a ) = f ( b ). } = = similar relations = = = = = approximate equality = = = numerical analysis is the study of constructive methods and algorithms to find numerical approximations ( as opposed to symbolic manipulations ) of solutions to problems in mathematical analysis. especially those which cannot be solved analytically. calculations are likely to involve rounding errors and other approximation errors. log tables, slide rules, and calculators produce approximate answers to all but the simplest calculations. the results of computer calculations are normally an approximation, expressed in a limited number of significant digits, although they can be programmed to produce more precise results. if viewed as a binary relation, ( denoted by the symbol ≈ { \ displaystyle \ approx } ) between real numbers or other things, if precisely defined, is not an equivalence relation since it ' s not transitive, even if modeled as a fuzzy relation. in computer science, equality is given by some relational operator. real | https://en.wikipedia.org/wiki/Equality_(mathematics) |
the phase transitions in the transverse field ising model in a competing spatially modulated ( periodic and oscillatory ) longitudinal field are studied numerically. there is a multiphase point in absence of the transverse field where the degeneracy for a longitudinal field of wavelength $ \ lambda $ is $ ( \ frac { 1 + \ sqrt { 5 } } { 2 } ) ^ { 2n / \ lambda } $ for a system with $ n $ spins, an exact result obtained from the known result for $ \ lambda = 2 $. the phase transitions in the $ \ gamma $ ( transverse field ) versus $ h _ 0 $ ( amplitude of the longitudinal field ) phase diagram are obtained from the vanishing of the mass gap $ \ delta $. we find that for all the phase transition points obtained in this way, $ \ delta $ shows finite size scaling behaviour signifying a continuous phase transition everywhere. the values of the critical exponents show that the model belongs to the universality class of the two dimensional ising model. the longitudinal field is found to have the same scaling behaviour as that of the transverse field, which seems to be a unique feature for the competing field. the phase boundaries for two different wavelengths of the modulated field are obtained. close to the multiphase point at $ h _ c $, the phase boundary behaves as $ ( h _ c - h _ 0 ) ^ b $, where $ b $ is also $ \ lambda $ dependent. | arxiv:cond-mat/0010246 |
we propose a new approach to the problem of rapidity gap survival ( rgs ) in the production of high - mass systems ( h = dijet, heavy quarkonium, higgs boson ) in double - gap exclusive diffractive pp scattering, pp - > p + ( gap ) + h + ( gap ) + p. it is based on the idea that hard and soft interactions proceed over widely different time - and distance scales and are thus approximately independent. the high - mass system is produced in a hard scattering process with exchange of two gluons between the protons. its amplitude is calculable in terms of the gluon generalized parton distributions ( gpds ) in the protons, which can be measured in j / psi production in exclusive ep scattering. the hard scattering process is modified by soft spectator interactions, which we calculate in a model - independent way in terms of the pp elastic scattering amplitude. contributions from inelastic intermediate states are suppressed. a simple geometric picture of the interplay of hard and soft interactions in diffraction is obtained. the onset of the black - disk limit in pp scattering at tev energies strongly suppresses diffraction at small impact parameters and is the main factor in determining the rgs probability. correlations between hard and soft interactions ( e. g. due to scattering from the long - range pion field of the proton, or due to possible short - range transverse correlations between partons ) further decrease the rgs probability. we also investigate the dependence of the diffractive cross section on the transverse momenta of the final - state protons ( " diffraction pattern " ). by measuring this dependence one can perform detailed tests of the interplay of hard and soft interactions, and even extract information about the gluon gpd in the proton. such studies appear to be feasible with the planned forward detectors at the lhc. | arxiv:hep-ph/0608271 |
compact matrix quantum groups act naturally on cuntz algebras. the first author isolated certain conditions under which the fixed point algebras under this action are kirchberg algebras. hence they are completely determined by their $ k $ - groups. building on prior work by the second author, we prove that free easy quantum groups satisfy these conditions and we compute the $ k $ - groups of their fixed point algebras in a general form. we then turn to examples such as the quantum permutation group $ s _ n ^ + $, the free orthogonal quantum group $ o _ n ^ + $ and the quantum reflection groups $ h _ n ^ { s + } $. our fixed point - algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups, which are related to hopf - galois extensions. | arxiv:1606.00569 |
a block of rubber eventually buckles under severe flexure, and several axial wrinkles appear on the inner curved face of the bent block. experimental measurements reveal that the buckling occurs earlier - - - at lower compressive strains - - - than expected from theoretical predictions. this paper shows that if rubber is modeled as being bimodular, and specifically, as being stiffer in compression than in tension, then flexure bifurcation happens indeed at lower levels of compressive strain than predicted by previous investigations ( these included taking into account finite size effects, compressibility effects, and strain - stiffening effects. ) here the effect of bimodularity is investigated within the theory of incremental buckling, and bifurcation equations, numerical methods, dispersion curves, and field variations are presented and discussed. it is also seen that finite element analysis software seems to be unable to encompass in a realistic manner the phenomenon of bending instability for rubber blocks. | arxiv:1301.5437 |
a zero - sum two person perfect information stochastic game ( pisg ) under limiting average payoff has a value and both the maximiser and the minimiser have optimal pure stationary strategies. firstly we form the matrix of undiscounted payoffs corresponding to each pair of pure stationary strategies ( for each initial state ) of the two players and prove that this matrix has a pure saddle point. then by using the results by derman [ 1 ] we prove the existence of optimal pure stationary strategy pair of the players. a crude but finite step algorithm is given to compute such an optimal pure stationary strategy pair of the players. | arxiv:2302.07151 |
the impact of new stellar evolution models with rotation on the predictions of population synthesis models is discussed. massive rotating stars have larger convective cores than their non - rotating counterparts, and their outer layers are chemically enriched due to increased mixing. together, these two effects lead to hotter and more luminous stars, in particular during later evolutionary phases. as a result, stellar populations containing massive stars are predicted to become more luminous for a given mass and to emit more ionizing photons. depending on the assumed rotation velocity, rotation causes profound changes in the properties of young stellar populations. these changes are most noticeable at later evolutionary phases and at shorter wavelengths of the spectral energy distribution. most strikingly, the lyman continuum luminosity increases by up to a factor of five in o - and wolf - rayet stars. care is required when comparing these models to observations, and some fine - tuning of the models is still required before recalibrations of star - formation indicators should be attempted. | arxiv:1402.0824 |
we present the results from a detailed x - ray variability analysis of 66 agn in the lockman hole, which have optical spectroscopic identifications. we compare, quantitatively, their variability properties with the properties of local agn, and we study the " variability - luminosity " relation as a function of redshift, and the " variability - redshift " relation in two luminosity bins. we use archival data from the last 10 xmm observations of the lockman hole field to extract light curves in the rest frame, 2 - 10 kev band. we use the " normalized excess variance " to quantify the variability amplitude. using the latest results regarding the agn power spectral shape and its dependence on black hole mass and accretion rate, we are able to compute model " variability - luminosity " curves, which we compare with the relations we observe. when we consider all the sources in our sample, we find that their variability amplitude decreases with increasing redshift and luminosity. these global anti - correlations are less pronounced when we split the objects in various luminosity and redshift bins. we do not find a significant correlation between variability amplitude and spectral slope. the " variability - luminosity " relation that we detect has a larger amplitude when compared to that of local agn. we also find that, at a given luminosity, the variability amplitude increases with redshift up to z ~ 1, and then stays roughly constant. our results imply that the agn x - ray mechanism operates in the same way at all redshifts. among objects with the same luminosity in our sample, the black hole mass decreases and the accretion rate increases with larger redshift. | arxiv:0805.2851 |
we investigate projection methods, for evaluating a linear approximation of the value function of a policy in a markov decision process context. we consider two popular approaches, the one - step temporal difference fix - point computation ( td ( 0 ) ) and the bellman residual ( br ) minimization. we describe examples, where each method outperforms the other. we highlight a simple relation between the objective function they minimize, and show that while br enjoys a performance guarantee, td ( 0 ) does not in general. we then propose a unified view in terms of oblique projections of the bellman equation, which substantially simplifies and extends the characterization of ( schoknecht, 2002 ) and the recent analysis of ( yu & bertsekas, 2008 ). eventually, we describe some simulations that suggest that if the td ( 0 ) solution is usually slightly better than the br solution, its inherent numerical instability makes it very bad in some cases, and thus worse on average. | arxiv:1011.4362 |
topological entanglement entropy ( tee ), the sub - leading term in the entanglement entropy of topological order, is the direct evidence of the long - range entanglement. while effective in characterizing topological orders on closed manifolds, tee is model - dependent when entanglement cuts intersect with physical gapped boundaries. in this paper, we study the origin of this model - dependence by introducing a model - independent picture of partitioning the topological orders with gapped boundaries. in our picture, the entanglement boundaries ( ebs ), i. e. the virtual boundaries of each subsystem induced by the entanglement cuts, are assumed to be gapped boundaries with boundary defects. at this model - independent stage, there are two choices one has to make manually in defining the bi - partition : the boundary condition on the ebs, and the coherence between certain boundary states. we show that tee appears because of a constraint on the defect configurations on the ebs, which is choice - dependent in the cases where the ebs touch gapped boundaries. this choice - dependence is known as the ambiguity in entanglement entropy. different models intrinsically employ different choices, rendering tee model - dependent. for z2 toric code, the ambiguity can be fully characterized by two parameters that respectively quantifies the eb condition and the coherence. in particular, calculations compatible with the folding trick naturally choose eb conditions that respect electric - magnetic duality and set specific parameter values. | arxiv:2311.17569 |
predictions for angular correlations between an arbitrary number of partons are derived in the high energy limit. the quantities considered depend on angles and primary energy through a single variable $ \ epsilon $ which implies certain scaling properties and relations between quite different observables. these asymptotic predictions derived in the double log approximation of qcd are checked against monte carlo calculations at the parton and hadron level. | arxiv:hep-ph/9501326 |
deep supervised hashing for image retrieval has attracted researchers ' attention due to its high efficiency and superior retrieval performance. most existing deep supervised hashing works, which are based on pairwise / triplet labels, suffer from the expensive computational cost and insufficient utilization of the semantics information. recently, deep classwise hashing introduced a classwise loss supervised by class labels information alternatively ; however, we find it still has its drawback. in this paper, we propose an improved deep classwise hashing, which enables hashing learning and class centers learning simultaneously. specifically, we design a two - step strategy on center similarity learning. it interacts with the classwise loss to attract the class center to concentrate on the intra - class samples while pushing other class centers as far as possible. the centers similarity learning contributes to generating more compact and discriminative hashing codes. we conduct experiments on three benchmark datasets. it shows that the proposed method effectively surpasses the original method and outperforms state - of - the - art baselines under various commonly - used evaluation metrics for image retrieval. | arxiv:2103.09442 |
we present a numerical method to estimate the lensing parameters and the hubble constant h _ 0 from quadruply imaged gravitational lens systems. the lens galaxy is modeled using both separable deflection potentials and constant mass - to - light ratio profiles, while possible external perturbations have been taken into account introducing an external shear. the model parameters are recovered inverting the lens and the time delay ratio equations and imposing a set of physically motivated selection criteria. we investigate correlations among the model parameters and the hubble constant. finally, we apply the codes to the real lensed quasars pg 1115 + 080 and rx j0911 + 0551, and combine the results from these two systems to get h _ 0 = 56 + / - 23 km / ( s mpc ). in addition, we are able to fit to the single systems a general elliptical potential with a non fixed angular part, and then we model the two lens systems with the same potential and a shared h _ 0 : in this last case we estimate h _ 0 = 49 _ ( - 11 ) ^ ( + 6 ) km / ( s mpc ). | arxiv:astro-ph/0407134 |
the reactivity of water vapor introduced in an atmospheric dielectric barrier discharge supplied in argon is investigated through optical emission spectroscopy measurements. this discharge is also used for the treatment of ldpe surfaces. water contact angles measurements, xps and afm techniques are used to study the grafting of oxygen functions on the ldpe surface and increase its hydrophilicity. | arxiv:1604.08795 |
we investigate gate - defined quantum dots in silicon on insulator nanowire field - effect transistors fabricated using a foundry - compatible fully - depleted silicon - on - insulator ( fd - soi ) process. a series of split gates wrapped over the silicon nanowire naturally produces a $ 2 \ times n $ bilinear array of quantum dots along a single nanowire. we begin by studying the capacitive coupling of quantum dots within such a 2 $ \ times $ 2 array, and then show how such couplings can be extended across two parallel silicon nanowires coupled together by shared, electrically isolated, ' floating ' electrodes. with one quantum dot operating as a single - electron - box sensor, the floating gate serves to enhance the charge sensitivity range, enabling it to detect charge state transitions in a separate silicon nanowire. by comparing measurements from multiple devices we illustrate the impact of the floating gate by quantifying both the charge sensitivity decay as a function of dot - sensor separation and configuration within the dual - nanowire structure. | arxiv:2005.14712 |
the article presents a new interpretation for zipf - mandelbrot ' s law in natural language which rests on two areas of information theory. firstly, we construct a new class of grammar - based codes and, secondly, we investigate properties of strongly nonergodic stationary processes. the motivation for the joint discussion is to prove a proposition with a simple informal statement : if a text of length $ n $ describes $ n ^ \ beta $ independent facts in a repetitive way then the text contains at least $ n ^ \ beta / \ log n $ different words, under suitable conditions on $ n $. in the formal statement, two modeling postulates are adopted. firstly, the words are understood as nonterminal symbols of the shortest grammar - based encoding of the text. secondly, the text is assumed to be emitted by a finite - energy strongly nonergodic source whereas the facts are binary iid variables predictable in a shift - invariant way. | arxiv:0810.3125 |
we consider a differential equation driven by a brownian motion as well as a rough path. we prove a girsanov - type result for this equation to construct a weak solution in the probabilistic sense. | arxiv:1805.01243 |
we present analyses from a real - time information monitoring system of online local news in the u. s. we study relationships among online local news coverage of covid, cases and deaths in an area, and properties of local news outlets and their audiences. our analysis relies on a unique dataset of the online content of over 300 local news outlets, encompassing over 750, 000 articles over a period of 10 months spanning april 2020 to february 2021. we find that the rate of covid coverage over time by local news outlets was primarily associated with death rates at the national level, but that this effect dissipated over the course of the pandemic as news about covid was steadily displaced by sociopolitical events, like the 2020 u. s. elections. we also find that both the volume and content of covid coverage differed depending on local politics, and outlet audience size, as well as evidence that more vulnerable populations received less pandemic - related news. | arxiv:2111.08515 |
the exact entropy of two - charge supersymmetric black holes in n = 4 string theories is computed to all orders using wald ' s formula and the supersymmetric attractor equations with an effective action that includes the relevant higher curvature terms. classically, these black holes have zero area but the attractor equations are still applicable at the quantum level. the quantum corrected macroscopic entropy agrees precisely with the microscopic counting for an infinite tower of fundamental string states to all orders in an asymptotic expansion. | arxiv:hep-th/0409148 |
in this article we study quasilinear multipower systems of two equations of two types, in a domain $ \ omega $ of r ^ { n } : with absorption terms, or mixed terms. despite of the lack of comparison principle, we prove a priori estimates of keller - osserman type. concerning the mixed system, we show that one of the solutions always satisfies harnack inequality. in the case $ \ omega $ = b ( 0, 1 ) \ { 0 }, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. finally we prove the sharpness of the results. | arxiv:1102.2564 |
annihilation of extremely energetic cosmic neutrinos on the relic - neutrino background can give rise to absorption lines at energies corresponding to formation of the electroweak gauge boson $ z ^ { 0 } $. the positions of the absorption dips are set by the masses of the relic neutrinos. suitably intense sources of extremely energetic ( $ 10 ^ { 21 } $ - - $ 10 ^ { 25 } $ - ev ) cosmic neutrinos might therefore enable the determination of the absolute neutrino masses and the flavor composition of the mass eigenstates. several factors - - other than neutrino mass and composition - - distort the absorption lines, however. we analyze the influence of the time - evolution of the relic - neutrino density and the consequences of neutrino decay. we consider the sensitivity of the lineshape to the age and character of extremely energetic neutrino sources, and to the thermal history of the universe, reflected in the expansion rate. we take into account fermi motion arising from the thermal distribution of the relic - neutrino gas. we also note the implications of dirac vs. majorana relics, and briefly consider unconventional neutrino histories. we ask what kinds of external information would enhance the potential of cosmic - neutrino absorption spectroscopy, and estimate the sensitivity required to make the technique a reality. | arxiv:hep-ph/0412122 |
efficient and accurate extraction of microstructures in micrographs of materials is essential in process optimization and the exploration of structure - property relationships. deep learning - based image segmentation techniques that rely on manual annotation are laborious and time - consuming and hardly meet the demand for model transferability and generalization on various source images. segment anything model ( sam ), a large visual model with powerful deep feature representation and zero - shot generalization capabilities, has provided new solutions for image segmentation. in this paper, we propose matsam, a general and efficient microstructure extraction solution based on sam. a simple yet effective point - based prompt generation strategy is designed, grounded on the distribution and shape of microstructures. specifically, in an unsupervised and training - free way, it adaptively generates prompt points for different microscopy images, fuses the centroid points of the coarsely extracted region of interest ( roi ) and native grid points, and integrates corresponding post - processing operations for quantitative characterization of microstructures of materials. for common microstructures including grain boundary and multiple phases, matsam achieves superior zero - shot segmentation performance to conventional rule - based methods and is even preferable to supervised learning methods evaluated on 16 microscopy datasets whose micrographs are imaged by the optical microscope ( om ) and scanning electron microscope ( sem ). especially, on 4 public datasets, matsam shows unexpected competitive segmentation performance against their specialist models. we believe that, without the need for human labeling, matsam can significantly reduce the cost of quantitative characterization and statistical analysis of extensive microstructures of materials, and thus accelerate the design of new materials. | arxiv:2401.05638 |
this report provides a description of unbunched beam stochastic cooling in the framework of control theory. the main interest in the investigation is concentrated on the beam stability in an active cooling system. a stochastic cooling system must be considered as a closed - loop, similar to the feedback systems used to damp collective instabilities. these systems, which are able to act upon themselves, are potentially unstable. the self - consistent solution for the beam motion is derived by means of a mode analysis of the collective beam motion. this solution yields a criterion for the stability of each collective mode. the expressions also allow for overlapping frequency bands in the beam spectrum and thus are valid over the entire frequency range. having established the boundaries of stability in this way, the fokker - planck equation is used to describe the cooling process. this description does not include collective effects and thus a stable beam must be assumed. hence the predictions about the cooling process following from the fokker - planck equation only make physical sense within the boundaries of beam stability. finally it is verified that the parameters of the cooling system which give the best cooling results are compatible with the stability of the beam. | arxiv:acc-phys/9607001 |
the dynamics of an inviscid and incompressible fluid flow on a riemannian manifold is governed by the euler equations. recently, tao launched a programme to address the global existence problem for the euler and navier stokes equations based on the concept of universality. inspired by this proposal, in this article we prove that the stationary euler equations exhibit several universality features. more precisely, we show that any non - autonomous flow on a compact manifold can be extended to a smooth stationary solution of the euler equations on some riemannian manifold of possibly higher dimension. the solutions we construct are of beltrami type, and being stationary they exist for all time. using this result, we establish the turing completeness of the steady euler flows, i. e., there exist solutions that encode a universal turing machine and, in particular, these solutions have undecidable trajectories. our proofs deepen the correspondence between contact topology and hydrodynamics, which is key to establish the universality of the reeb flows and their beltrami counterparts. an essential ingredient in the proofs, of interest in itself, is a novel flexibility theorem for embeddings in reeb dynamics in terms of an h - principle in contact geometry, which unveils the flexible behavior of the steady euler flows. these results can be viewed as lending support to the intuition that solutions to the euler equations can be extremely complicated in nature. | arxiv:1911.01963 |
the traditional presentation of unimodular gravity ( ug ) consists on indicating that it is an alternative theory of gravity that restricts the generic diffeomorphism invariance of general relativity. in particular, as often encountered in the literature, unlike general relativity, unimodular gravity is invariant solely under volume - preserving diffeomorphisms. that characterization of ug has led to some confusion and incorrect statements in various treatments on the subject. for instance, sometimes it is claimed ( mistakenly ) that only spacetime metrics such that $ | $ det $ g _ { \ mu \ nu } | = 1 $ can be considered as valid solutions of the theory. additionally, that same ( incorrect ) statement is often invoked to argue that some particular gauges ( e. g. the newtonian or synchronous gauge ) are not allowed when dealing with cosmological perturbation theory in ug. the present article is devoted to clarify those and other misconceptions regarding the notion of diffeomorphism invariance, in general, and its usage in the context of ug, in particular. | arxiv:2308.07360 |
we report the result of a search for neutrinos in coincidence with solar flares from the goes flare database. the search was performed on a 10. 8 kton - year exposure of kamland collected from 2002 to 2019. this large exposure allows us to explore previously unconstrained parameter space for solar flare neutrinos. we found no statistical excess of neutrinos and established 90 % confidence level upper limits of $ 8. 4 \ times 10 ^ 7 $ cm $ ^ { - 2 } $ ( $ 3. 0 \ times 10 ^ { 9 } $ cm $ ^ { - 2 } $ ) on electron anti - neutrino ( electron neutrino ) fluence at 20 mev normalized to the x12 flare, assuming that the neutrino fluence is proportional to the x - ray intensity. | arxiv:2105.02458 |
we examine an extension of the sm higgs sector by a higgs triplet taking into consideration the higgs - like particle discovery at the lhc with mass around 125 gev. we evaluate the bounds on the scalar potential through the unitarity of the scattering - matrix. considering with and without $ \ z _ 2 $ - symmetry on the extra triplet, we derive constraints on the parameter space. we identify the region of the parameter space that corresponds to the stability and metastability of the electroweak vacuum. we also show that at large field values the scalar potential of this model is suitable to explain inflation. | arxiv:1610.03178 |
we consider a novel mechanism to realize exothermic dark matter with dark mesons in the limit of approximate flavor symmetry in a dark qcd. we introduce a local dark $ u ( 1 ) ' $ symmetry to communicate between dark mesons and the standard model via $ z ' $ portal by partially gauging the dark flavor symmetry with flavor - dependent charges for cancelling chiral anomalies in the dark sector. after the dark local $ u ( 1 ) ' $ is broken spontaneously by the vev of a dark higgs, there appear small mass splittings between dark quarks, consequently, leading to small split masses for dark mesons, required to explain the electron recoil excess in xenon1t by the inelastic scattering between dark mesons and electron. we propose a concrete benchmark model for split dark mesons based on $ su ( 3 ) _ l \ times su ( 3 ) _ r / su ( 3 ) _ v $ flavor symmetry and $ su ( n _ c ) $ color group and show that there exists a parameter space making a better fit to the xenon1t data with two correlated peaks from exothermic processes and satisfying the correct relic density, current experimental and theoretical constraints. | arxiv:2012.03713 |
it is shown that isospin - breaking corrections to the pion - deuteron scattering length can be very large, because of the vanishing of the isospin - symmetric contribution to this scattering length at leading order in chiral perturbation theory. we further demonstrate that these corrections can explain the bulk of the discrepancy between the recent experimental data on pionic hydrogen and pionic deuterium. we also give the first determination of the electromagnetic low - energy constant f1. | arxiv:nucl-th/0512035 |
we show that the balance between localized gain and nonlinear cubic dissipation in the twodimensional nonlinear schrodinger equation allows for existence of stable two - dimensional localized modes which we identify as solitons. such modes exist only when the gain is strong enough and the energy flow exceeds certain threshold value. the observed solitons neither undergo diffractive spreading nor collapse. above the critical value of the gain the symmetry breaking occurs and asymmetric dissipative solitons emerge. | arxiv:1012.0844 |
the unitarity in lorentz invariance violating qed consisting of standard fermions and higher - order photons of the myers - pospelov theory is studied. we find ghost states associated to the higher - order character of the theory which could render the $ s $ matrix nonunitary. an explicit calculation to check perturbative unitarity in the process of electron - positron scattering is performed and it is found to be possible to preserve unitarity. | arxiv:1307.5340 |
the first comprehensive study of electron gains and losses in hypersonic air flows including the full coupling between the non - neutral plasma sheaths and the quasi - neutral plasma flow is here presented. such is made possible by the use of advanced numerical methods that overcome the stiffness associated with the plasma sheaths. the coupling between the sheaths, the electron temperature in non - equilibrium, and the ambipolar diffusion within the quasi - neutral plasma flow is found to be critical to predict accurately electron losses and, thus, plasma density around hypersonic vehicles. this is because electron cooling coming from the non - neutral sheaths affects significantly electron temperature everywhere in the plasma and, therefore, the electron - temperature - dependent loss processes of ambipolar diffusion and dissociative recombination. results obtained show that electron loss to the surface due to catalyticity dominates over electron loss within the plasma due to dissociative recombination either ( i ) at high altitude where the dynamic pressure is low, or ( ii ) at low mach number, or ( iii ) when the vehicle has a sharp leading edge. | arxiv:2111.09432 |
this paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. we show that clarkson ' s sampling algorithm can be applied to two problems in computational algebra : solving large - scale polynomial systems and finding small generating sets of graded ideals. the cornerstone of our work is showing that the theory of violator spaces of g \ " artner et al. \ applies to polynomial ideal problems. to show this, one utilizes a helly - type result for algebraic varieties. the resulting algorithms have expected runtime linear in the number of input polynomials, making the ideas interesting for handling systems with very large numbers of polynomials, but whose rank in the vector space of polynomials is small ( e. g., when the number of variables and degree is constant ). | arxiv:1503.08804 |
mass loss is a key process in the evolution of massive stars, and must be understood quantitatively to be successfully included in broader astrophysical applications. in this review, we discuss various aspects of radiation driven mass loss, both from the theoretical and the observational side. we focus on winds from ob - stars, with some excursions to the luminous blue variables, wolf - rayet stars, a - supergiants and central stars of planetary nebulae. after reca - pitulating the 1 - d, stationary standard model of line - driven wind, extensions accounting for rotation and magnetic fields are discussed. the relevance of the so - called bi - stability jump is outlined. we summarize diagnostical methods to infer wind properties from observations, and compare the results with theore - tical predictions, featuring the massloss - metallicity dependence. subsequently, we concentrate on two urgent problems which challenge our present understanding of radiation driven winds : weak winds and wind - clumping. we discuss problems of measuring mass - loss rates from weak winds and the potential of nir - spectroscopy. wind - clumping has severe implications for the interpretation of observational diagnostics, as derived mass - loss rates can be overestimated by factors of 2 to 10 if clumping is ignored, and we describe ongoing attempts to allow for more uniform results. we point out that independent arguments from stellar evolution favor a moderate reduction of present - day mass - loss rates. we also consider larger scale wind structure, interpreted in terms of co - rotating interacting regions, and complete this review with a discussion of recent progress on the x - ray line emission from massive stars, highlighting as to how far the analysis of such x - ray line emission can give further clues regarding an adequate description of wind clumping. ( abridged abstract ) | arxiv:0811.0487 |
we performed two - dimensional molecular dynamics simulations of cohesive disks under shear. the cohesion between the disks is added by the action of springs between very next neighbouring disks, modelling capillary forces. the geometry of the cell allows disk - disk shearing and not disk - cell wall shearing as it is commonly found in literature. does a stick - slip phenomenon happen though the upper cover moves at a constant velocity, i. e. with an infinite shearing force? we measured the forces acted by the disks on the upper cover for different shearing rates, as well as the disk velocities as a function of the distance to the bottom of the cell. it appears that the forces measured versus time present a periodic behavior, very close to a stick slip phenomenon, for shearing rates larger than a given threshold. the disks ' collective displacements in the shearing cell ( back and ahead ) is the counterpart of the constant velocity of the upper cover leading to a periodic behavior of the shear stress. | arxiv:cond-mat/0505231 |
gy { \ ' a } rf { \ ' a } s et al. and zaker have proven that the grundy number of a graph $ g $ satisfies $ \ gamma ( g ) \ ge t $ if and only if $ g $ contains an induced subgraph called a $ t $ - atom. the family of $ t $ - atoms has bounded order and contains a finite number of graphs. in this article, we introduce equivalents of $ t $ - atoms for b - coloring and partial grundy coloring. this concept is used to prove that determining if $ \ varphi ( g ) \ ge t $ and $ \ partial \ gamma ( g ) \ ge t $ ( under conditions for the b - coloring ), for a graph $ g $, is in xp with parameter $ t $. we illustrate the utility of the concept of $ t $ - atoms by giving results on b - critical vertices and edges, on b - perfect graphs and on graphs of girth at least $ 7 $. | arxiv:1505.07780 |
we consider the hadroproduction of w gauge bosons in their leptonic decay mode. starting from the leading - order expressions, we show that by defining a suitable scaling variable the centre - of - mass dependence of the cross sections at the lhc energies can be essentially described by a simple power law. the scaling exponent is directly linked to the small - $ x $ behaviour of parton distribution functions ( pdf ) which, at the high virtualities involved in w production, is largely dictated by qcd evolution equations. this entails a particularly simple scaling law for the lepton charge asymmetry and also predicts that measurements in different collision systems ( p - p, p - $ \ bar { \ rm p } $, p - pb pb - pb ) are straightforwardly related. the expectations are compared with the existing data and a very good overall agreement is observed. it is shown that the pdf uncertainty in certain cross - section ratios between nearby centre - of - mass energies can be significantly reduced by taking the ratios at fixed value of scaling variable instead of fixed rapidity. | arxiv:1509.03993 |
quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. here we propose and theoretically investigate a new quantum interferometric scheme based on three - dimensional waveguide devices. these can be implemented by femtosecond laser waveguide writing, recently adopted for quantum applications. in particular, multiarm interferometers include " tritter " and " quarter " as basic elements, corresponding to the generalization of a beam splitter to a 3 - and 4 - port splitter, respectively. by injecting fock states in the input ports of such interferometers, fringe patterns characterized by nonclassical visibilities are expected. this enables outperforming the quantum fisher information obtained with classical fields in phase estimation. we also discuss the possibility of achieving the simultaneous estimation of more than one optical phase. this approach is expected to open new perspectives to quantum enhanced sensing and metrology performed in integrated photonic. | arxiv:1301.1577 |
we adopt the viewpoint that topological and \ ' e - quillen theory for commutative $ s $ - algebras should provide usable ( co ) homology theories for doing calculations in the sense traditional within algebraic topology. our main emphasis is on homotopical properties of universal derivations, especially their behaviour in multiplicative homology theories. there are algebraic derivation properties, but also deeper properties arising from the homotopical structure of the free algebra functor $ \ mathbb { p } _ r $ and its relationship with extended powers of spectra. in the connective case in ordinary $ \ bmod { \, p } $ homology, this leads to useful formulae involving dyer - lashof operations in the homology of commutative $ s $ - algebras. although many of our results could no doubt be obtained using stabilisation, our approach seems more direct. we also discuss a reduced free algebra functor $ \ tilde { \ mathbb { p } } _ r $. | arxiv:1208.1868 |
it is proved that there exists a separable reflexive banach space w that contains an isomorphic image of every separable superreflexive banach space. this gives the affirmative answer on one j. bourgain ' s question | arxiv:math/0206010 |
in power grids, short - term load forecasting ( stlf ) is crucial as it contributes to the optimization of their reliability, emissions, and costs, while it enables the participation of energy companies in the energy market. stlf is a challenging task, due to the complex demand of active and reactive power from multiple types of electrical loads and their dependence on numerous exogenous variables. amongst them, special circumstances, such as the covid - 19 pandemic, can often be the reason behind distribution shifts of load series. this work conducts a comparative study of deep learning ( dl ) architectures, namely neural basis expansion analysis time series forecasting ( n - beats ), long short - term memory ( lstm ), and temporal convolutional networks ( tcn ), with respect to forecasting accuracy and training sustainability, meanwhile examining their out - of - distribution generalization capabilities during the covid - 19 pandemic era. a pattern sequence forecasting ( psf ) model is used as baseline. the case study focuses on day - ahead forecasts for the portuguese national 15 - minute resolution net load time series. the results can be leveraged by energy companies and network operators ( i ) to reinforce their forecasting toolkit with state - of - the - art dl models ; ( ii ) to become aware of the serious consequences of crisis events on model performance ; ( iii ) as a high - level model evaluation, deployment, and sustainability guide within a smart grid context. | arxiv:2302.13046 |
the tor network has been a significant part of the internet for years. tor was originally started in the naval research laboratory for anonymous internet browsing and internet - based communication. from being used for anonymous communications, it has now segmented into various other use - cases like censorship circumvention, performing illegal activities, etc. in this paper, we perform empirical measurements on the tor network to analyze the trends in tor over the years. we gather our measurements data through our measurement scripts, past research in this domain, and aggregated data provided by the tor metrics directory. we use this data to analyze trends and understand the incidents that caused fluctuations in the trends of different data parameters. we collect measurements data for tor parameters like tor users, onion services, tor relays, and bridges, etc. we also study censorshiprelated events and study trends by analyzing censorship - related metrics. finally, we touch upon the location diversity in tor and study how the tor circuit selection and construction are impacted by the bandwidth distribution of tor relays across geographies. | arxiv:2208.11149 |
flat bands provide a natural platform for emergent electronic states beyond landau paradigm. among those of particular importance are flat chern bands, including bands of higher chern numbers ( $ c $ $ > $ $ 1 $ ). we introduce a new framework for band flatness through wave functions, and classify the existing isolated flat bands in a " periodic table " according to tight binding features and wave function properties. our flat band categorization encompasses seemingly different classes of flat bands ranging from atomic insulators to perfectly flat chern bands and landau levels. the perfectly flat chern bands satisfy berry curvature condition $ f _ { xy } = \ text { tr } \, \ mathcal g _ { ij } $ which on the tight - binding level is fulfilled only for infinite - range models. most of the natural chern bands fall into category of $ c = 1 $ ; the complexity of creating higher - $ c $ flat bands is beyond the current technology. this is due to the breakdown of the microscopic stability for higher - $ c $ flatness, seen atomistically e. g. in the increase of the hopping range bound as $ \ propto $ $ \ sqrt { c } a $. within our new formalism, we indicate strategies for bypassing higher - $ c $ constraints and thus dramatically decreasing the implementation complexity. | arxiv:2105.14672 |
two important classes of the quantum statistical model, the locally quasi - classical model and the quasi - classical model, are introduced from the estimation theoretical viewpoint, and they are characterized geometrically by the vanishing conditions of the relative phase factor ( rpf ), implying the close tie between uhlmann parallel transport and the quantum estimation theory. | arxiv:quant-ph/9711027 |
behavior recognition is an important task in video representation learning. an essential aspect pertains to effective feature learning conducive to behavior recognition. recently, researchers have started to study fine - grained behavior recognition, which provides similar behaviors and encourages the model to concern with more details of behaviors with effective features for distinction. however, previous fine - grained behaviors limited themselves to controlling partial information to be similar, leading to an unfair and not comprehensive evaluation of existing works. in this work, we develop a new video fine - grained behavior dataset, named bear, which provides fine - grained ( i. e. similar ) behaviors that uniquely focus on two primary factors defining behavior : environment and action. it includes two fine - grained behavior protocols including fine - grained behavior with similar environments and fine - grained behavior with similar actions as well as multiple sub - protocols as different scenarios. furthermore, with this new dataset, we conduct multiple experiments with different behavior recognition models. our research primarily explores the impact of input modality, a critical element in studying the environmental and action - based aspects of behavior recognition. our experimental results yield intriguing insights that have substantial implications for further research endeavors. | arxiv:2503.20209 |
we present results of a chandra survey of the ultra - luminous x - ray sources ( ulx ) in 13 normal galaxies, in which we combine source detection with x - ray flux measurement. 22 ulx were detected, i. e. with l _ x > 1 x 10 ^ { 39 } erg s ^ { - 1 } ( l _ 10 ), and 39 other sources were detected with l _ x > 5 x 10 ^ { 38 } erg s ^ { - 1 } ( l _ 5 ). we also use radial intensity profiles to remove extended sources from the sample. the majority of sources are not extended, which for a typical distance constrains the emission region size to less than 50 pc. x - ray colour - colour diagrams and spectral fitting results were examined for indicators of the ulx nature. in the case of the brighter sources, spectral fitting generally requires two - component models. in only a few cases do colour - colour diagrams or spectral fitting provide evidence of black hole nature. we find no evidence of a correlation with stellar mass, however there is a strong correlation with star formation as indicated by the 60 micron flux as found in previous studies. | arxiv:astro-ph/0305345 |
we study the decays of $ b _ { ( s ) } $ mesons into light pseudoscalar mesons under the $ su ( 3 ) $ flavour symmetry. assuming exact $ su ( 3 ) $ symmetry at the level of the amplitudes leads to a simple parameterization. using the available experimental data and, for the first time, mixing effects in the $ b _ s ^ 0 $ decays, we find that the data cannot be described with this assumption. we improve this parametrization by including { \ it factorizable } $ su ( 3 ) _ \ mathrm { f } $ - breaking effects. this new approach allows for an excellent description of the data, with a fit $ p $ value of $ 32. 3 \ % $. we provide posterior predictions for all observables and identify several decay channels that would significantly impact our analysis. finally, we briefly compare our results with the predictions of qcd factorization, paving the way to a more detailed analysis which could provide insights into qcd effects at low energy scales. | arxiv:2504.05209 |
we provide ongoing results from the development of a personalized learning system integrated into a serious game. given limited instructor resources, the use of computerized systems to help tutor students offers a way to provide higher quality education and to improve educational efficacy. personalized learning systems like the one proposed in this paper offer an accessible solution. furthermore, by combining such a system with a serious game, students are further engaged in interacting with the system. the proposed learning system combines expert - driven structure and lesson planning with computational intelligence methods and gamification to provide students with a fun and educational experience. as the project is ongoing from past years, numerous design iterations have been made on the system based on feedback from students and classroom observations. using computational intelligence, the system adaptively provides support to students based on data collected from both their in - game actions and by estimating their emotional state from webcam images. for our evaluation, we focus on student data gathered from in - classroom testing in relevant courses, with both educational efficacy, results and student observations. to demonstrate the effect of our proposed system, students in an early electrical engineering course were instructed to interact with the system in place of a standard lab assignment. the system would then measure and help them improve their background knowledge before allowing them to complete the lab assignment. as they played through the game, we observed their interactions with the system to gather insights for future work. additionally, we demonstrate the system ' s educational efficacy through pre - post - test results from students who played the game with and without the personalized learning system. | arxiv:2305.16568 |
in this paper, we propose an image re - sampling compression method by learning virtual codec network ( vcn ) to resolve the non - differentiable problem of quantization function for image compression. here, the image re - sampling not only refers to image full - resolution re - sampling but also low - resolution re - sampling. we generalize this method for standard - compliant image compression ( scic ) framework and deep neural networks based compression ( dnnc ) framework. specifically, an input image is measured by re - sampling network ( rsn ) network to get re - sampled vectors. then, these vectors are directly quantized in the feature space in scic, or discrete cosine transform coefficients of these vectors are quantized to further improve coding efficiency in dnnc. at the encoder, the quantized vectors or coefficients are losslessly compressed by arithmetic coding. at the receiver, the decoded vectors are utilized to restore input image by image decoder network ( idn ). in order to train rsn network and idn network together in an end - to - end fashion, our vcn network intimates projection from the re - sampled vectors to the idn - decoded image. as a result, gradients from idn network to rsn network can be approximated by vcn network ' s gradient. because dimension reduction can be further achieved by quantization in some dimensional space after image re - sampling within auto - encoder architecture, we can well initialize our networks from pre - trained auto - encoder networks. through extensive experiments and analysis, it is verified that the proposed method has more effectiveness and versatility than many state - of - the - art approaches. | arxiv:1806.08514 |
applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. thus, applied mathematics is a combination of mathematical science and specialized knowledge. the term " applied mathematics " also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. in the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. the activity of applied mathematics is thus intimately connected with research in pure mathematics. = = history = = historically, applied mathematics consisted principally of applied analysis, most notably differential equations ; approximation theory ( broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis ) ; and applied probability. these areas of mathematics related directly to the development of newtonian physics, and in fact, the distinction between mathematicians and physicists was not sharply drawn before the mid - 19th century. this history left a pedagogical legacy in the united states : until the early 20th century, subjects such as classical mechanics were often taught in applied mathematics departments at american universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments. engineering and computer science departments have traditionally made use of applied mathematics. as time passed, applied mathematics grew alongside the advancement of science and technology. with the advent of modern times, the application of mathematics in fields such as science, economics, technology, and more became deeper and more timely. the development of computers and other technologies enabled a more detailed study and application of mathematical concepts in various fields. today, applied mathematics continues to be crucial for societal and technological advancement. it guides the development of new technologies, economic progress, and addresses challenges in various scientific fields and industries. the history of applied mathematics continually demonstrates the importance of mathematics in human progress. = = divisions = = today, the term " applied mathematics " is used in a broader sense. it includes the classical areas noted above as well as other areas that have become increasingly important in applications. even fields such as number theory that are part of pure mathematics are now important in applications ( such as cryptography ), though they are not generally considered to be part of the field of applied mathematics per se. there is no consensus as to what the various branches of applied mathematics are. such categorizations are made difficult by the way mathematics and science change over time, and also by the way universities organize departments, | https://en.wikipedia.org/wiki/Applied_mathematics |
we show that any compact half - conformally flat manifold of negative type, with bounded $ l ^ 2 $ energy, sufficiently small scalar curvature, and a non - collapsing assumption, has all betti numbers bounded. we show that this result is optimal from an analytic perspective by demonstrating singularity models that are 2 - ended, and are asymptotically k \ " ahler on both ends. we show that bounded self - dual solutions of $ d \ omega = 0 $ on ale manifold ends are either asymptotically k \ " ahler, or they have a decay rate of $ o ( r ^ { - 4 } ) $ or better. | arxiv:1907.09025 |
we study counterintuitive dynamics of a two - level system ( tls ) interacting with electric field superoscillating in time. we show that a tls may be excited by an external light pulse whose spectral components are below the absorption line of the tls. we attribute this unique dynamics to the rabi oscillations of the tls in a superoscillating driving field. | arxiv:1409.5644 |
this paper presents a novel methodology for fast simulation and analysis of transient heat transfer. the proposed methodology is suitable for real - time applications owing to ( i ) establishing the solution method from the viewpoint of computationally efficient explicit dynamics, ( ii ) proposing an element - level thermal load computation to eliminate the need for assembling global thermal stiffness, leading to ( iii ) an explicit formulation of nodal temperature computation to eliminate the need for iterations anywhere in the algorithm, ( iv ) pre - computing the constant matrices and simulation parameters to facilitate online calculation, and ( v ) utilising computationally efficient finite elements to efficiently obtain thermal responses in the spatial domain, all of which lead to a significant reduction in computation time for fast run - time simulation. the proposed fast explicit dynamics finite element algorithm ( fed - fem ) employs nonlinear thermal material properties, such as temperature - dependent thermal conductivity and specific heat capacity, and nonlinear thermal boundary conditions, such as heat convection and radiation, to account for nonlinear characteristics of transient heat transfer. simulations and comparison analyses demonstrate that not only can the proposed methodology handle isotropic, orthotropic, anisotropic and temperature - dependent thermal properties but also satisfy the standard patch tests and achieve good agreement with those of the commercial finite element analysis packages for numerical accuracy, for 3 - d heat conduction, convection, radiation, and thermal gradient concentration problems. furthermore, the proposed fed - fem algorithm is computationally efficient and only consumes a small computation time, capable of achieving real - time computational performance, leading to a novel methodology suitable for real - time simulation and analysis of transient heat transfer. | arxiv:1909.03355 |
in this work, the univariant two - phase coexistence line of the hydrate of tetrahydrofuran ( thf ) is determined from 100 to 1000 bar by molecular dynamics simulations. the study is carried out by putting in contact a thf hydrate phase with a stoichiometric aqueous solution phase. following the direct coexistence technique, the pressure has been fixed, and the coexistence line has been determined by analyzing if the hydrate phase grows or melts at different values of temperature. the model of water used is the well - known tip4p / ice model. we have used two different models of thf based on the transferable parameters for phase equilibria - united atom approach ( trappe - ua ), the original ( flexible ) trappe - ua model as well as a rigid and planar version of it. overall, at high pressures, small differences have been observed in the results obtained by both models. also, large differences have been observed in the computational efforts required by the simulations performed using both models, being the rigid and planar version much faster than the original one. the effect of the unlike dispersive interactions between the water and thf molecules has been also analyzed at 250 bar using the rigid and planar thf model. in particular, we have modified the berthelot combining rule by adding a factor ( { \ xi } o - thf ) that modifies the unlike water - thf dispersive interactions and we have analyzed the effect on the dissociation temperature when { \ xi } o - thf is modified from 1. 0 ( original berthelot combining rule ) to 1. 4 ( modified berthelot combining rule ). we have extended the study using { \ xi } o - thf = 1. 4 and the rigid thf model to the rest of the pressures considered in this work, finding an excellent agreement with the scarce experimental data taken from the literature. | arxiv:2405.04887 |
the path packing problem is stated finding the maximum number of edge - disjoint paths between predefined pairs of nodes in an undirected multigraph. such a multigraph together with predefined node pairs is often called a network. | arxiv:0912.1452 |
fully - supervised polyp segmentation has accomplished significant triumphs over the years in advancing the early diagnosis of colorectal cancer. however, label - efficient solutions from weak supervision like scribbles are rarely explored yet primarily meaningful and demanding in medical practice due to the expensiveness and scarcity of densely - annotated polyp data. besides, various deployment issues, including data shifts and corruption, put forward further requests for model generalization and robustness. to address these concerns, we design a framework of spatial - spectral dual - branch mutual teaching and entropy - guided pseudo label ensemble learning ( s $ ^ 2 $ me ). concretely, for the first time in weakly - supervised medical image segmentation, we promote the dual - branch co - teaching framework by leveraging the intrinsic complementarity of features extracted from the spatial and spectral domains and encouraging cross - space consistency through collaborative optimization. furthermore, to produce reliable mixed pseudo labels, which enhance the effectiveness of ensemble learning, we introduce a novel adaptive pixel - wise fusion technique based on the entropy guidance from the spatial and spectral branches. our strategy efficiently mitigates the deleterious effects of uncertainty and noise present in pseudo labels and surpasses previous alternatives in terms of efficacy. ultimately, we formulate a holistic optimization objective to learn from the hybrid supervision of scribbles and pseudo labels. extensive experiments and evaluation on four public datasets demonstrate the superiority of our method regarding in - distribution accuracy, out - of - distribution generalization, and robustness, highlighting its promising clinical significance. our code is available at https : / / github. com / lofrienger / s2me. | arxiv:2306.00451 |
difference hierarchies were originally introduced by hausdorff and they play an important role in descriptive set theory. in this survey paper, we study difference hierarchies of regular languages. the first sections describe standard techniques on difference hierarchies, mostly due to hausdorff. we illustrate these techniques by giving decidability results on the difference hierarchies based on shuffle ideals, strongly cyclic regular languages and the polynomial closure of group languages. | arxiv:1702.08023 |
we briefly review the state - of - the - art in phase - field modeling of microstructure evolution. the focus is placed on recent applications of phase - field simulations of solid - state microstructure evolution and solidification that have been compared and / or validated with experiments. they show the potential of phase - field modeling to make quantitative predictions of the link between processing and microstructure. finally, some current challenges in extending the application of phase - field models within the context of integrated computational materials engineering are mentioned. | arxiv:2104.09915 |
by utilizing the idea of colombeau ' s generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. the category consisting of diffeological spaces and asymptotic maps is enriched over the category of diffeological spaces, and inherits completeness and cocompleteness. in particular, the set of asymptotic functions on a euclidean open set include schwartz distributions and form a colombeau type smooth differential algebra over robinson ' s field of asymptotic numbers. to illustrate the usefulness of our machinery, we show that homotopy extension property can be established for smooth relative cell complexes if we exploit asymptotic maps instead of smooth ones. | arxiv:2002.11339 |
dissipation induced by interactions with an external environment typically hinders the performance of quantum computation, but in some cases can be turned out as a useful resource. we show the potential enhancement induced by dissipation in the field of quantum reservoir computing introducing tunable local losses in spin network models. our approach based on continuous dissipation is able not only to reproduce the dynamics of previous proposals of quantum reservoir computing, based on discontinuous erasing maps but also to enhance their performance. control of the damping rates is shown to boost popular machine learning temporal tasks as the capability to linearly and non - linearly process the input history and to forecast chaotic series. finally, we formally prove that, under non - restrictive conditions, our dissipative models form a universal class for reservoir computing. it means that considering our approach, it is possible to approximate any fading memory map with arbitrary precision. | arxiv:2212.12078 |
the spin effect of electrons / positrons ( $ e ^ - $ / $ e ^ + $ ) and polarization effect of $ \ gamma $ photons are investigated in the interaction of two counter - propagating linearly polarized 10 - pw - class laser pulses with a thin foil target. the processes of nonlinear compton scattering and nonlinear breit - wheeler pair production based on spin - and polarization - resolved probabilities are implemented into the particle - in - cell ( pic ) algorithm by monte carlo methods. it is found from pic simulations that the average degree of linear polarization of emitted $ \ gamma $ photons can exceed $ 50 \ % $. this polarization effect leads to reduced positron yield by about $ 10 \ % $. at some medium positron energies, the reduction can reach $ 20 \ % $. furthermore, we also observe that the local spin polarization of $ e ^ - $ / $ e ^ + $ leads to a slight decrease of the positron yield about $ 2 \ % $ and some anomalous phenomena about the positron spectrum and photon polarization at the high - energy range, due to spin - dependent photon emissions. our results indicate that spin and polarization effects should be considered in calculating the pair production and laser - plasma interaction with the laser power of 10 - pw class. | arxiv:2102.05882 |
in stoc ' 95 [ admss ' 95 ] arya et al. showed that any set of $ n $ points in $ \ mathbb r ^ d $ admits a $ ( 1 + \ epsilon ) $ - spanner with hop - diameter at most 2 ( respectively, 3 ) and $ o ( n \ log n ) $ edges ( resp., $ o ( n \ log \ log n ) $ edges ). they also gave a general upper bound tradeoff of hop - diameter at most $ k $ and $ o ( n \ alpha _ k ( n ) ) $ edges, for any $ k \ ge 2 $. the function $ \ alpha _ k $ is the inverse of a certain ackermann - style function at the $ \ lfloor k / 2 \ rfloor $ th level of the primitive recursive hierarchy, where $ \ alpha _ 0 ( n ) = \ lceil n / 2 \ rceil $, $ \ alpha _ 1 ( n ) = \ left \ lceil \ sqrt { n } \ right \ rceil $, $ \ alpha _ 2 ( n ) = \ lceil \ log { n } \ rceil $, $ \ alpha _ 3 ( n ) = \ lceil \ log \ log { n } \ rceil $, $ \ alpha _ 4 ( n ) = \ log ^ * n $, $ \ alpha _ 5 ( n ) = \ lfloor \ frac { 1 } { 2 } \ log ^ * n \ rfloor $, \ ldots. roughly speaking, for $ k \ ge 2 $ the function $ \ alpha _ { k } $ is close to $ \ lfloor \ frac { k - 2 } { 2 } \ rfloor $ - iterated log - star function, i. e., $ \ log $ with $ \ lfloor \ frac { k - 2 } { 2 } \ rfloor $ stars. also, $ \ alpha _ { 2 \ alpha ( n ) + 4 } ( n ) \ le 4 $, where $ \ alpha ( n ) $ is the one - parameter inverse ackermann function, which is an extremely slowly growing function. whether or not this tradeoff is tight has remained open, even for the cases $ k = 2 $ and $ k = 3 $. two lower bounds are known : the first applies only to spanners with stretch 1 and the second is sub - optimal and | arxiv:2112.09124 |
particle correlations and fluctuations measured by rhic experiments at $ \ sqrt { s _ { nn } } $ = 130 gev were discussed. the source size parameters were similar to those measured at the cern - sps, and no long duration time of particle emission were observed. it was pointed out that the dependences of longitudinal and transverse radius parameters on the pair momentum are explained with a single $ m _ t $ scaling function observed at the sps energy. fluctuation studies of mean $ p _ { t } $ of charged particles and of mean $ e _ { t } $ in an electromagnetic calorimeter found no significant non - statistical fluctuations by phenix, but some indication in charge independent $ < p _ t > $ by star. | arxiv:hep-ph/0111460 |
the $ \ lambda $ - $ \ lambda $ effective interaction, in the channel $ l = s = 0 $, in the nuclear medium is fitted to the available binding energies, $ b _ { \ lambda \ lambda } $, of double $ \ lambda $ hypernuclei : $ ^ { 6 } _ { \ lambda \ lambda } $ he, $ ^ { 10 } _ { \ lambda \ lambda } $ be and $ ^ { 13 } _ { \ lambda \ lambda } $ b. the mesonic decay of these hypernuclei is also investigated. finally, this effective interaction is used to predict the binding energies and mesonic decays widths of heavier double $ \ lambda $ hypernuclei. | arxiv:nucl-th/9711035 |
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