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the semi - classical spectrum of the homogeneous sine - gordon theories associated with an arbitrary compact simple lie group g is obtained and shown to be entirely given by solitons. these theories describe quantum integrable massive perturbations of gepner ' s g - parafermions whose classical equations - of - motion are non - abelian affine toda equations. one - soliton solutions are constructed by embeddings of the su ( 2 ) complex sine - gordon soliton in the regular su ( 2 ) subgroups of g. the resulting spectrum exhibits both stable and unstable particles, which is a peculiar feature shared with the spectrum of monopoles and dyons in n = 2 and n = 4 supersymmetric gauge theories.
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arxiv:hep-th/9706203
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in this work, we exhaustively investigate $ 1 \ rightarrow 2 $ local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement ( geometric discord ) using asymmetric pauli cloners with most general two qubit state as the resource. we exemplify asymmetric broadcasting of entanglement using maximally entangled mixed states. we demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. we show that it is impossible to optimally broadcast geometric discord with the help of these asymmetric pauli cloning machines. we also study the problem of $ 1 \ rightarrow 3 $ broadcasting of entanglement using non - maximally entangled state ( nme ) as the resource. for this task, we introduce a method we call successive broadcasting which involves application of $ 1 \ rightarrow 2 $ optimal cloning machines multiple times. we compare and contrast the performance of this method with the application of direct $ 1 \ rightarrow 3 $ optimal cloning machines. we show that $ 1 \ rightarrow 3 $ optimal cloner does a better job at broadcasting than the successive application of $ 1 \ rightarrow 2 $ cloners and the successive method can be beneficial in the absence of $ 1 \ rightarrow 3 $ cloners. we also bring out the fundamental difference between the tasks of cloning and broadcasting in the final part of the manuscript. we create examples to show that there exist local unitaries which can be employed to give a better range for broadcasting. such unitary operations are not only economical, but also surpass the best possible range obtained using existing cloning machines enabling broadcasting of lesser entangled states. this result opens up a new direction in exploration of methods to facilitate broadcasting which may outperform the standard strategies implemented through cloning transformations.
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arxiv:1702.02123
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in precision crop protection, ( target - orientated ) object detection in image processing can help navigate unmanned aerial vehicles ( uav, crop protection drones ) to the right place to apply the pesticide. unnecessary application of non - target areas could be avoided. deep learning algorithms dominantly use in modern computer vision tasks which require high computing time, memory footprint, and power consumption. based on the edge artificial intelligence, we investigate the main three paths that lead to dealing with this problem, including hardware accelerators, efficient algorithms, and model compression. finally, we integrate them and propose a solution based on a light deep neural network ( dnn ), called ag - yolo, which can make the crop protection uav have the ability to target detection and autonomous operation. this solution is restricted in size, cost, flexible, fast, and energy - effective. the hardware is only 18 grams in weight and 1. 5 watts in energy consumption, and the developed dnn model needs only 838 kilobytes of disc space. we tested the developed hardware and software in comparison to the tiny version of the state - of - art yolov3 framework, known as yolov3 - tiny to detect individual palm in a plantation. an average f1 score of 0. 9205 at the speed of 36. 5 frames per second ( in comparison to similar accuracy at 18 frames per second and 8. 66 megabytes of the yolov3 - tiny algorithm ) was reached. this developed detection system is easily plugged into any machines already purchased as long as the machines have usb ports and run linux operating system.
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arxiv:2103.04132
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we introduce the weibull distribution as a simple parametrization of charged particle multiplicities in hadron - hadron collisions at all available energies, ranging from isr energies to the most recent lhc energies. in statistics, the weibull distribution has wide applicability in natural processes involving fragmentation processes. this gives a natural connection to the available state - of - the - art models for multi - particle production in hadron hadron collisions involving qcd parton fragmentation and hadronization.
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arxiv:1409.5831
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we classify completely the surfaces of general type whose canonical map is 3 - to - 1 onto a surface of minimal degree in projective space. these surfaces fall into 5 distinct classes and we give explicit examples belonging to each of these classes. as far as we know, one of the examples thus constructed was unknown and it is a surface whose canonical system has two infinitely near base points.
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arxiv:math/9807006
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##c12 | s | $ is very large.
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arxiv:1910.11807
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a key building block in the design of ultra - reliable communication systems is a wireless channel model that captures the statistics of rare events occurring due to significant fading. in this paper, we propose a novel methodology based on extreme value theory ( evt ) to statistically model the behavior of extreme events in a wireless channel for ultra - reliable communication. this methodology includes techniques for fitting the lower tail distribution of the received power to the generalized pareto distribution ( gpd ), determining the optimum threshold over which the tail statistics are derived, ascertaining the optimum stopping condition on the number of samples required to estimate the tail statistics by using gpd, and finally, assessing the validity of the derived pareto model. based on the data collected within the engine compartment of fiat linea under various engine vibrations and driving scenarios, we demonstrate that the proposed methodology provides the best fit to the collected data, significantly outperforming the conventional extrapolation - based methods. moreover, the usage of the evt in the proposed method decreases the required number of samples for estimating the tail statistics by about $ 7 \ times 10 ^ 5 $.
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arxiv:2002.00565
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we present the results of high - resolution ( r $ \ ge $ 30, 000 ) optical and near - infrared spectroscopic monitoring observations of a fu orionis - type object, v960 mon, which underwent an outburst in 2014 november. we have monitored this object with the bohyunsan optical echelle spectrograph ( boes ) and the immersion grating infrared spectrograph ( igrins ) since 2014 december. various features produced by a wind, disk, and outflow / jet were detected. the wind features varied over time and continually weakened after the outburst. we detected double - peaked line profiles in the optical and near - infrared, and the line widths tend to decrease with increasing wavelength, indicative of keplerian disk rotation. the disk features in the optical and near - infrared spectra fit well with g - type and k - type stellar spectra convolved with a kernel to account for the maximum projected disk rotation velocity of about 40. 3 $ \ pm $ 3. 8 km s $ ^ { - 1 } $ and 36. 3 $ \ pm $ 3. 9 km s $ ^ { - 1 } $, respectively. we also report the detection of [ s ii ] and h $ _ { 2 } $ emission lines, which are jet / outflow tracers and rarely found in fuors.
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arxiv:2007.03197
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in this paper we establish a comparison result through symmetrization for solutions to some boundary value problems involving the fractional laplacian. this allows to get sharp estimates for the solutions, obtained by comparing them with solutions of suitable radial problems. furthermore, we use such result to prove a priori estimates for solutions in terms of the data, providing several regularity results which extend the well known ones for the classical laplacian.
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arxiv:1106.0997
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we report on the observation of gate - tunable proximity - induced superconductivity and multiple andreev reflections ( mar ) in a bulk - insulating bisbtese $ _ 2 $ topological insulator nanoribbon ( tinr ) josephson junction ( jj ) with superconducting nb contacts. we observe a gate - tunable critical current ( $ i _ c $ ) for gate voltages ( $ v _ g $ ) above the charge neutrality point ( $ v _ { cnp } $ ), with $ i _ c $ as large as 430 na. we also observe mar peaks in the differential conductance ( $ di / dv $ ) versus dc voltage ( $ v _ { dc } $ ) across the junction corresponding to sub - harmonic peaks ( at $ v _ { dc } = v _ n = 2 \ delta _ { nb } / en $, where $ \ delta _ { nb } $ is the superconducting gap of the nb contacts and $ n $ is the sub - harmonic order ). the sub - harmonic order, $ n $, exhibits a $ v _ g $ - dependence and reaches $ n = 13 $ for $ v _ g = 40 $ v, indicating the high transparency of the nb contacts to tinr. our observations pave the way toward exploring the possibilities of using tinr in topologically protected devices that may host exotic physics such as majorana fermions.
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arxiv:1710.03362
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in non - canonical two - field inflation models, deviations from the canonical model can be captured by a parameter $ \ xi $. we show this parameter is usually one half of the slow - roll order and analytically calculate the primordial power spectra accurate to order $ \ xi ^ 2 $. the super - horizon perturbations are studied with an improved method, which gives a correction of order $ \ xi ^ 2 $. three typical examples demonstrate that our analytical formulae of power spectra fit well with numerical simulation.
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arxiv:1603.09567
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quantum secret sharing is a way to share secret messages among the clients in a group with complete security. for the first time, hillery et al. ( phys rev a 59 : 1829, 1999 ) proposed the quantum version of the classical secret sharing protocol using ghz states. here, we implement the above quantum secret sharing protocol in ' ibm q 5 tenerife ' quantum processor and compare the experimentally obtained results with the theoretically predicted ones. further, a new quantum binary voting protocol is proposed and implemented in the 14 - qubit ' ibm q 14 melbourne ' quantum processor. the results are analyzed through the technique of quantum state tomography, and the fidelity of states is calculated for a different number of executions made in the device.
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arxiv:1807.03219
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we study an extension of the so - called defective galton - watson processes obtained by allowing the offspring distribution to change over the generations. thus, in these processes, the individuals reproduce independently of the others and in accordance to some possibly defective offspring distribution depending on the generation. moreover, the defect $ 1 - f _ n ( 1 ) $ of the offspring distribution at generation $ n $ represents the probability that the process hits an absorbing state $ \ delta $ at that generation. we focus on the asymptotic behaviour of these processes. we establish the almost sure convergence of the process to a random variable with values in $ \ mathbb { n } _ 0 \ cup \ { \ delta \ } $ and we provide two characterisations of the duality extinction - absorption at $ \ delta $. we also state some results on the absorption time and the properties of the process conditioned upon its non - absorption, some of which require us to introduce the notion of defective branching trees in varying environment.
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arxiv:2011.08949
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the decay mode $ b _ s \ to \ psi \ overline { k } ^ * $ is suggested as a very good way to measure the $ b _ s $ mixing parameter $ x _ s $. these decays can be gathered using a $ \ psi \ to \ ell ^ + \ ell ^ - $ trigger. this final state has a well resolved four track decay vertex, useful for good time resolution and background rejection.
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arxiv:hep-ex/9509006
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in this article we apply an l - system to prove a recurrence formula for the length of the boundary of iterands of the well known harter - heighway dragon curve, a space filling curve with fractal boundary. this leads to finding formulas for related sequences of certain binary strings and ternary matrices. this proves some long standing conjectures for the recurrence relation for the number of terms in the boundary of the dragon curve, first stated in unpublished work daykin and tucker in 1975.
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arxiv:2407.17326
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we report a formation of sharp, solitonlike structures in an experimentally accessible ultracold fermi gas, as a quantum carpet solution is analyzed in a many body system. the effect is perfectly coherent in a noninteracting gas, but in the presence of repulsive interaction in a two - component system, the structures vanish at a finite time. as they disappear, the system enters a dynamical equilibrium, in which kinetic energies of atoms tend to the same average value. the coherence is revived in a strong interaction regime, with the onset of phase separation, and with a double quantum carpet appearing.
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arxiv:1811.05867
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theoretical investigations of different routes to coherent perfect polarization rotation illustrate its phenomenological connection with coherent perfect absorption. studying systems with broken parity, layering, combined faraday rotation and optical activity, or a rotator - loaded optical cavity highlights their similarity and suggests new approaches to improving and miniaturizing optical devices.
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arxiv:1412.8744
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many semantics for weighted argumentation frameworks assume that each argument is associated with an initial weight. however, eliciting these initial weights poses challenges : ( 1 ) accurately providing a specific numerical value is often difficult, and ( 2 ) individuals frequently confuse initial weights with acceptability degrees in the presence of other arguments. to address these issues, we propose an elicitation pipeline that allows one to specify acceptability degree intervals for each argument. by employing gradual semantics, we can refine these intervals when they are rational, restore rationality when they are not, and ultimately identify possible initial weights for each argument.
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arxiv:2502.07452
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we rigorously prove the existence of directed transport for a certain class of ac - driven nonlinear one dimensional systems, namely the generation of transport with a preferred direction in the absence of a net driving force.
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arxiv:0810.4414
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this paper is concerned with the study of one - body dissipation effects in idealized models resembling a nucleus. in particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a bunimovich stadium billiard. our results are twofold. first, we develop a method to solve in a simple way the quantum mechanical evolution of planar billiards with moving walls. the formalism is based on the { \ it scaling method } \ cite { ver } which enables the resolution of the problem in terms of quantities defined over the boundary of the billiard. the second result is related to the quantum aspects of dissipation in systems with complex spectra. we conclude that in a slowly varying evolution the energy is transferred from the boundary to the particle through landau $ - $ zener transitions.
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arxiv:chao-dyn/9608011
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systems are commonly monitored for health and security through collection and streaming of multivariate time series. advances in time series forecasting due to adoption of multilayer recurrent neural network architectures make it possible to forecast in high - dimensional time series, and identify and classify novelties early, based on subtle changes in the trends. however, mainstream approaches to multi - variate time series predictions do not handle well cases when the ongoing forecast must include uncertainty, nor they are robust to missing data. we introduce a new architecture for time series monitoring based on combination of state - of - the - art methods of forecasting in high - dimensional time series with full probabilistic handling of uncertainty. we demonstrate advantage of the architecture for time series forecasting and novelty detection, in particular with partially missing data, and empirically evaluate and compare the architecture to state - of - the - art approaches on a real - world data set.
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arxiv:2203.04916
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in this work, we propose a new soft - in soft - out decoder called soft - output from covered space ( socs ) decoder. it estimates the a posteriori reliability based on the space explored by a list decoder, i. e., the set of vectors for which the list decoder knows whether they are codewords. this approach enables a more accurate calculation of the a posteriori reliability and results in gains of up to 0. 25 $ \, $ db for turbo product decoding with socs compared to chase - pyndiah decoding.
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arxiv:2504.15204
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this paper explores the task of leveraging typology in the context of cross - lingual dependency parsing. while this linguistic information has shown great promise in pre - neural parsing, results for neural architectures have been mixed. the aim of our investigation is to better understand this state - of - the - art. our main findings are as follows : 1 ) the benefit of typological information is derived from coarsely grouping languages into syntactically - homogeneous clusters rather than from learning to leverage variations along individual typological dimensions in a compositional manner ; 2 ) typology consistent with the actual corpus statistics yields better transfer performance ; 3 ) typological similarity is only a rough proxy of cross - lingual transferability with respect to parsing.
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arxiv:1909.09279
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in recent years, there has been a surge of interest in exploring higher - order topology and their semi - metallic counterparts, particularly in the context of dirac and weyl semimetals, termed as higher - order dirac semimetal ( hodsm ) and higher - order weyl semimetal ( howsm ). the hodsm phase exhibits hinge fermi arcs ( fas ) with a quantized higher - order topological invariant. conversely, the howsm phase is a hybrid - order topological phase manifesting both surface and hinge fas as a signature of first - and second - order topology and also possesses both first - and second - order topological invariants. in this work, we investigate a tight binding model for multi - hodsm ( mhodsm ) hosting multiple hinge fas having a quantized quadrupolar winding number ( qwn ) greater than one. furthermore, we obtain a multi - howsm ( mhowsm ) phase from the mhodsm by applying an external magnetic field. the mhowsm phase possesses both the dipolar winding number being the representative invariant for first - order topology, and the qwn, featuring both surface and multiple hinge fas. we study the spectral properties of the mhodsm and mhowsm in different geometries. we also investigate the hinge fa - mediated transport in mhowsm employing a two - terminal setup.
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arxiv:2408.17152
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we propose a method of diagnostic of a degenerate ground state of bose condensate in a double well potential. the method is based on the study of the one - particle coherent tunneling under switching the time - dependent weak josephson coupling between the wells. we obtain a simple expression that allows to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of the particles in two wells $ \ delta n = n _ 1 - n _ 2 $ measured before the josephson coupling is switched on and after it is switched off. the specifics of the application of the method in the cases of the external and the internal josephson effect are discussed.
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arxiv:cond-mat/0406182
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the effect of the uniform magnetic field on the electron in the spherically symmetric square - well potential is studied. a transcendental equation that determines the electron energy spectrum is derived. the approximate value of the lowest ( bound ) energy state is found. the approximate wave function and probability current density of this state are constructed.
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arxiv:quant-ph/0703058
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the discovery of new families of exfoliatable 2d crystals that have diverse sets of electronic, optical, and spin - orbit coupling properties, enables the realization of unique physical phenomena in these few - atom thick building blocks and in proximity to other materials. herein, using nasn2as2 as a model system, we demonstrate that layered zintl phases having the stoichiometry att2pn2 ( a = group 1 or 2 element, tt = group 14 tetrel element and pn = group 15 pnictogen element ) and feature networks separated by van der waals gaps can be readily exfoliated with both mechanical and liquid - phase methods. we identified the symmetries of the raman active modes of the bulk crystals via polarized raman spectroscopy. the bulk and mechanically exfoliated nasn2as2 samples are resistant towards oxidation, with only the top surface oxidizing in ambient conditions over a couple of days, while the liquid - exfoliated samples oxidize much more quickly in ambient conditions. employing angle - resolved photoemission spectroscopy ( arpes ), density functional theory ( dft ), and transport on bulk and exfoliated samples, we show that nasn2as2 is a highly conducting 2d semimetal, with resistivities on the order of 10 - 6 { \ omega } m. due to peculiarities in the band structure, the dominating p - type carriers at low temperature are nearly compensated by the opening of n - type conduction channels as temperature increases. this work further expands the family of exfoliatable 2d materials to layered van der waals zintl phases, opening up opportunities in electronics and spintronics.
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arxiv:1710.09059
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recent observations of binary stars in the galactic field show that the binary fraction and the mean orbital separation both decrease as a function of decreasing primary mass. we present $ n $ - body simulations of the effects of dynamical evolution in star - forming regions on primordial binary stars to determine whether these observed trends can be explained by the dynamical processing of a common binary population. we find that dynamical processing of a binary population with an initial binary fraction of unity and an initial excess of intermediate / wide separation ( 100 - 10 $ ^ 4 $ au ) binaries does not reproduce the observed properties in the field, even in initially dense ( $ \ sim 10 ^ 3 $ m $ _ \ odot $ pc $ ^ { - 3 } $ ) star - forming regions. if instead we adopt a field - like population as the initial conditions, most brown dwarf and m - dwarf binaries are dynamically hard and their overall fractions and separation distributions are unaffected by dynamical evolution. g - dwarf and a - star binaries in the field are dynamically intermediate in our simulated dense regions and dynamical processing does destroy some systems with separations $ > $ 100 au. however, the formation of wide binaries through the dissolution of supervirial regions is a strong function of primary mass, and the wide g - dwarf and a - star binaries that are destroyed by dynamical evolution in subvirial regions are replenished by the formation of binaries in supervirial regions. we therefore suggest that the binary population in the field is $ indicative $ of the primordial binary population in star - forming regions, at least for systems with primary masses in the range 0. 02 - 3. 0m $ _ \ odot $.
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arxiv:1406.0844
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this work addresses the synthesis of optimal feedback control laws via machine learning. in particular, the averaged feedback learning scheme ( afls ) and a data driven method are considered. hypotheses for each method ensuring the convergence of the evaluation of the objective function of the underlying control problem at the obtained feedback - laws towards the optimal value function are provided. these hypotheses are connected to the regularity of the value function and the stability of the dynamics. in the case of afls these hypotheses only require h \ " older continuity of the value function, whereas for the data driven method the value function must be at least $ c ^ 2 $. it is demonstrated that these methods are connected via their optimality conditions. additionally, numerical experiments are provided by applying both methods to a family control problems, parameterized by a positive real number which controls the regularity of the value function. for small parameters the value function is smooth and in contrast for large parameters it is non - differentiable, but semi - concave. the results of the experiments indicate that both methods have a similar performance for the case that the value function is smooth. on the other hand, if the value function is not differentiable, afls has a better performance which is consistent with the obtained convergence results.
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arxiv:2407.18403
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an experimental proposal for realizing spin - orbit ( so ) coupling of pseudospin - 1 in the ground manifold $ ^ 1 \ sigma ( \ upsilon = 0 ) $ of ( bosonic ) bialkali polar molecules is presented. the three spin components are composed of the ground rotational state and two substates from the first excited rotational level. using hyperfine resolved raman processes through two select excited states resonantly coupled by a microwave, an effective coupling between the spin tensor and linear momentum is realized. the properties of bose - einstein condensates for such so - coupled molecules exhibiting dipolar interactions are further explored. in addition to the so - coupling - induced stripe structures, the singly and doubly quantized vortex phases are found to appear, implicating exciting opportunities for exploring novel quantum physics using so - coupled rotating polar molecules with dipolar interactions.
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arxiv:1805.05524
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we define a groupoid from a labelled space and show that it is isomorphic to the tight groupoid arising from an inverse semigroup associated with the labelled space. we then define a local homeomorphism on the tight spectrum that is a generalization of the shift map for graphs, and show that the defined groupoid is isomorphic to the renault - deaconu groupoid for this local homeomorphism. finally, we show that the c * - algebra of this groupoid is isomorphic to the c * - algebra of the labelled space as introduced by bates and pask.
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arxiv:1811.12754
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several authors have found a statistically significant excess of galaxies with higher redshifts relative to the group centre, so - called discordant redshifts, in particular in groups where the brightest galaxy, identified in apparent magnitudes, is a spiral. our aim is to explain the observed redshift excess. we use a semi - analytical galaxy catalogue constructed from the millennium simulation to study redshift asymmetries in spiral - dominated groups in the lambda cold dark matter ( lambdacdm ) cosmology. we show that discordant redshifts in small galaxy groups arise when these groups are gravitationally unbound and the dominant galaxy of the group is misidentified. the redshift excess is especially significant when the apparently brightest galaxy can be identified as a spiral, in full agreement with observations. on the other hand, the groups that are gravitationally bound do not show a significant redshift asymmetry. when the dominant members of groups in mock catalogues are identified by using the absolute b - band magnitudes, our results show a small blueshift excess. this result is due to the magnitude limited observations that miss the faint background galaxies in groups. when the group centre is not correctly identified it may cause the major part of the observed redshift excess. if the group is also gravitationally unbound, the level of the redshift excess becomes as high as in observations. there is no need to introduce any " anomalous " redshift mechanism to explain the observed redshift excess. further, as the friends - of - friends percolation algorithm picks out the expanding parts of groups, in addition to the gravitationally bound group cores, group catalogues constructed in this way cannot be used as if the groups are purely bound systems.
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arxiv:0811.3968
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recent measurements of baryon acoustic oscillations ( bao ) by the dark energy spectroscopic instrument ( desi ) suggest a preference for a dynamic dark energy model over a cosmological constant. this conclusion emerges from the combination of desi ' s bao data with observations of the cosmic microwave background ( cmb ) and various type ia supernova ( sn ia ) catalogues. the deviation observed in the cosmological constant ( $ \ lambda $ ) reflects a departure from the standard cosmological model. testing this deviation involves examining the consistency between cosmological parameters derived from early and late - time observations. specifically, we focus on the matter density parameter $ \ omega _ m = \ omega _ mh ^ 2 $ and introduce $ { \ rm ratio } ( \ omega _ m ) $ to assess consistency, which is defined as the ratio of $ \ omega _ m $ values constrained by high and low - redshift measurements. this ratio serves as a metric for quantifying deviations from the $ \ lambda $ cdm model. in this paper, we find that the desi bao + cmb yields $ { \ rm ratio } ( \ omega _ m ) = 1. 0171 \ pm0. 0066 $. upon excluding the lrg1 and lrg2 data in desi bao, this ratio adjusts to $ { \ rm ratio } ( \ omega _ m ) = 1. 0100 \ pm0. 0082 $. this shift, corresponding to a change from $ 2. 6 \ sigma $ to $ 1. 2 \ sigma $, indicates that the deviation from the $ \ lambda $ cdm model is predominantly driven by these two samples from the desi bao measurements. to substantiate this conclusion, we utilized two cosmological model - independent methods to reconstruct the cosmic expansion history. both reconstructions of the hubble parameter $ h ( z ) $ indicate that the evolving features of dark energy are determined by the combined lrg1 and lrg2 data. therefore, different methods have reached the same conclusion, namely the importance of accurately measuring the bao feature in lrg1 and lrg2 data.
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arxiv:2407.04385
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a trace - finite - cell - method for the numerical analysis of thin shells is presented combining concepts of the tracefem and the finite - cell - method. as an underlying shell model we use the koiter model, which we re - derive in strong form based on first principles of continuum mechanics by recasting well - known relations formulated in local coordinates to a formulation independent of a parametrization. the field approximation is constructed by restricting shape functions defined on a structured background grid on the shell surface. as shape functions we use on a background grid the tensor product of cubic splines. this yields $ c ^ 1 $ - continuous approximation spaces, which are required by the governing equations of fourth order. the parametrization - free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. furthermore, benchmark tests are investigated.
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arxiv:2007.00075
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a shape invariant nonseparable and nondiagonalizable two - dimensional model with anharmonic complex interaction, first studied by cannata, ioffe, and nishnianidze, is re - examined with the purpose of providing an algebraic construction of the associated functions to the excited - state wavefunctions, needed to complete the basis. the two operators $ a ^ + $ and $ a ^ - $, coming from the shape invariant supersymmetric approach, where $ a ^ + $ acts as a raising operator while $ a ^ - $ annihilates all wavefunctions, are completed by introducing a novel pair of operators $ b ^ + $ and $ b ^ - $, where $ b ^ - $ acts as the missing lowering operator. it is then shown that building the associated functions as polynomials in $ a ^ + $ and $ b ^ + $ acting on the ground state provides a much more efficient approach than that used in the original paper. in particular, we have been able to extend the previous results obtained for the first two excited states of the quartic anharmonic oscillator either by considering the next three excited states or by adding a cubic or a sextic term to the hamiltonian.
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arxiv:2111.01617
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multidimensional spectroscopy is becoming an increasingly popular tool and there is an ongoing effort to access electronic transitions and many - body dynamics in correlated materials. we apply the protocol recently proposed by wang to extract two - dimensional polaron spectra in a fermi superfluid with an impurity. the bath is descibed by a bcs ansatz and it assumed that the impurity can scatter at most one quasiparticle pair. the spectral response contains a symmetric contribution, which carries the same information as ramsey spectra, and an asymmetric one. while { \ it a priori } it may seem promising to probe the quasiparticle gap from the asymmetric contribution, we show explicitly that this is not the case and, in the absence of incoherent processes, multidimensional spectroscopy does not bring much additional information. our calculation is suitable for 3d ultracold gases, but we discuss implications for exciton - polarons in 2d materials.
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arxiv:2210.01174
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we study neutrinoless double beta decay in left - right symmetric extension of the standard model with type i and type ii seesaw origin of neutrino masses. due to the enhanced gauge symmetry as well as extended scalar sector, there are several new physics sources of neutrinoless double beta decay in this model. ignoring the left - right gauge boson mixing and heavy - light neutrino mixing, we first compute the contributions to neutrinoless double beta decay for type i and type ii dominant seesaw separately and compare with the standard light neutrino contributions. we then repeat the exercise by considering the presence of both type i and type ii seesaw, having non - negligible contributions to light neutrino masses and show the difference in results from individual seesaw cases. assuming the new gauge bosons and scalars to be around a tev, we constrain different parameters of the model including both heavy and light neutrino masses from the requirement of keeping the new physics contribution to neutrinoless double beta decay amplitude below the upper limit set by the gerda experiment and also satisfying bounds from lepton flavor violation, cosmology and colliders.
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arxiv:1509.01800
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while phase oscillators are often used to model neuronal populations, in contrast to the kuramoto paradigm, strong interactions between brain areas can be associated with loss of synchrony. using networks of coupled oscillators described by neural mass models, we find that a transition to decoherence at increased coupling strength results from the fundamental nonlinearity, e. g., arising from refractoriness, of the interactions between the nodes. the nonlinearity - driven transition also depends on the connection topology, underlining the role of network structure in shaping brain activity.
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arxiv:2011.05859
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this paper introduces the token space framework, a novel mathematical construct designed to enhance the interpretability and effectiveness of deep learning models through the application of category theory. by establishing a categorical structure at the token level, we provide a new lens through which ai computations can be understood, emphasizing the relationships between tokens, such as grouping, order, and parameter types. we explore the foundational methodologies of the token space, detailing its construction, the role of construction operators and initial categories, and its application in analyzing deep learning models, specifically focusing on attention mechanisms and transformer architectures. the integration of category theory into ai research offers a unified framework to describe and analyze computational structures, enabling new research paths and development possibilities. our investigation reveals that the token space framework not only facilitates a deeper theoretical understanding of deep learning models but also opens avenues for the design of more efficient, interpretable, and innovative models, illustrating the significant role of category theory in advancing computational models.
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arxiv:2404.11624
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the design, simulation, fabrication, calibration, and performance of the gluex start counter detector is described. the start counter was designed to operate at integrated rates of up to 9 mhz with a timing resolution in the range of 500 to 825 ps ( fwhm ). the start counter provides excellent solid angle coverage, a high degree of segmentation for background rejection, and can be utilized in the level 1 trigger for the experiment. it consists of a cylindrical array of 30 thin scintillators with pointed ends that bend towards the beam line at the downstream end. magnetic field insensitive silicon photomultiplier detectors were used as the light sensors.
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arxiv:1901.02759
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the kohn - sham ( ks ) system is an auxiliary system whose effective potential is unknown in most cases. it is in principle determined by the ground state density, and it has been found numerically for some low - dimensional systems by inverting the ks equations starting from a given accurate density. for solids, only approximate results are available. in this work, we determine accurate exchange correlation ( xc ) potentials for si and nacl using the ground state densities obtained from auxiliary field quantum monte carlo calculations. we show that these xc potentials can be rationalized as an ensemble of environment - adapted functions of the local density. the ks band structure can be obtained with high accuracy. the true ks band gap turns out to be larger than the prediction of the local density approximation, but significantly smaller than the measurable photoemission gap, which confirms previous estimates. finally, our findings show that the conjecture that very different xc potentials can lead to very similar densities and other ks observables is true also in solids, which questions the meaning of details of the potentials and, at the same time, confirms the stability of the ks system.
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arxiv:2207.03919
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the skewness of a graph g is the minimum number of edges in g whose removal results in a planar graph. by appropriately introducing a weight to each edge of a graph, we determine, among other thing, the skewness of the generalized petersen graph p ( 4k, k ) for odd k at least 9. this provides an answer to the conjecture raised in [ 3 ].
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arxiv:1709.06280
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we tackle the problem of discovering novel classes in an image collection given labelled examples of other classes. this setting is similar to semi - supervised learning, but significantly harder because there are no labelled examples for the new classes. the challenge, then, is to leverage the information contained in the labelled images in order to learn a general - purpose clustering model and use the latter to identify the new classes in the unlabelled data. in this work we address this problem by combining three ideas : ( 1 ) we suggest that the common approach of bootstrapping an image representation using the labeled data only introduces an unwanted bias, and that this can be avoided by using self - supervised learning to train the representation from scratch on the union of labelled and unlabelled data ; ( 2 ) we use rank statistics to transfer the model ' s knowledge of the labelled classes to the problem of clustering the unlabelled images ; and, ( 3 ) we train the data representation by optimizing a joint objective function on the labelled and unlabelled subsets of the data, improving both the supervised classification of the labelled data, and the clustering of the unlabelled data. we evaluate our approach on standard classification benchmarks and outperform current methods for novel category discovery by a significant margin.
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arxiv:2002.05714
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the popularity of tor as an anonymity system has made it a popular target for a variety of attacks. we focus on traffic correlation attacks, which are no longer solely in the realm of academic research with recent revelations about the nsa and gchq actively working to implement them in practice. our first contribution is an empirical study that allows us to gain a high fidelity snapshot of the threat of traffic correlation attacks in the wild. we find that up to 40 % of all circuits created by tor are vulnerable to attacks by traffic correlation from autonomous system ( as ) - level adversaries, 42 % from colluding as - level adversaries, and 85 % from state - level adversaries. in addition, we find that in some regions ( notably, china and iran ) there exist many cases where over 95 % of all possible circuits are vulnerable to correlation attacks, emphasizing the need for as - aware relay - selection. to mitigate the threat of such attacks, we build astoria - - an as - aware tor client. astoria leverages recent developments in network measurement to perform path - prediction and intelligent relay selection. astoria reduces the number of vulnerable circuits to 2 % against as - level adversaries, under 5 % against colluding as - level adversaries, and 25 % against state - level adversaries. in addition, astoria load balances across the tor network so as to not overload any set of relays.
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arxiv:1505.05173
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a bachelor of technology ( b. tech., b. t., or btech ; latin baccalaureus technologiae ) is a bachelor ' s academic degree that is awarded for an undergraduate program in engineering. = = australia = = in australia, the bachelor of technology ( btech ) degree is offered by rmit university, edith cowan university, curtin university and certain private institutions. = = canada = = in canada, the degree is offered by british columbia institute of technology, thompson rivers university, northern alberta institute of technology, mcmaster university, seneca college, algonquin college, and marine institute of memorial university of newfoundland. = = india = = bachelor of technology ( b. tech. ) degree in india is an undergraduate academic degree conferred after the completion of a four - year full - time engineering program from all india council for technical education recognised institute. the b. tech. degree is generally awarded by indian institutes of technology ( iits ), national institutes of technology ( nits ) ( india ), indian institutes of information technology ( iiits ), government funded technical institutes ( gftis ) or other centrally funded technical institutes ( cftis ) and private deemed universities in various engineering disciplines such as civil engineering, chemical engineering, mechanical engineering, electrical engineering, computer science and engineering, electronics and communication engineering, cyber security and many more. this degree is generally equivalent to a bachelor of engineering offered in other affiliated engineering colleges of state collegiate universities or a bachelor of science in engineering or bachelor of engineering in the united states and europe. eligibility for a b. tech. program in india typically requires candidates to have completed their higher secondary education ( 10 + 2 ) with mandatory subjects such as mathematics, physics, chemistry or other technical subjects. institutions often set a minimum aggregate percentage requirement, usually 75 % and the joint entrance examination ( jee ) main is a prominent entrance exam for b. tech. admissions, comprising questions in mathematics, physics and chemistry. jee advanced is the subsequent exam for those trying to enter the indian institutes of technology ( iits ). admission to national institutes of technology ( nits ), indian institutes of information technology ( iiits ), mit vishwaprayag university, solapur other government funded technical institutes ( gftis ) and deemed universities like amrita vishwa vidyapeetham, international institute of information technology, hyderabad are based on jee main scores. = = pakistan = = the national technology council ( ntc ) of pakistan is responsible for accrediting 4 - year
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https://en.wikipedia.org/wiki/Bachelor_of_Technology
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we investigate the effects of pre - hydrodynamic evolution on final - state observables in heavy - ion collisions using state - of - the art event simulations coupled to different pre - hydrodynamic scenarios, which include the recently - developed effective kinetic transport theory evolution model kompost. flow observables are found to be insensitive to the details of pre - hydrodynamic evolution. the main effect we observe is in the $ p _ t $ spectra, particularly the mean transverse momentum. however, at least part of this effect is a consequence of the underlying conformal invariance assumption currently present in such approaches, which is known to be violated in the temperature regime probed in heavy - ion collisions. this assumption of early time conformal invariance leads to an artificially large out - of - equilibrium bulk pressure when switching from ( conformal ) pre - hydrodynamic evolution to hydrodynamics ( using the non - conformal qcd equation of state ), which in turn increases the transverse momentum. our study indicates that a consistent treatment of pre - hydrodynamic evolution in heavy - ion collisions requires the use of non - conformal models of early time dynamics.
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arxiv:2006.02324
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motivated by a phenomenon of phase transition in a model of alignment of self - propelled particles, we obtain a kinetic mean - field equation which is nothing else than the doi equation ( also called smoluchowski equation ) with dipolar potential. in a self - contained article, using only basic tools, we analyze the dynamics of this equation in any dimension. we first prove global well - posedness of this equation, starting with an initial condition in any sobolev space. we then compute all possible steady - states. there is a threshold for the noise parameter : over this threshold, the only equilibrium is the uniform distribution, and under this threshold, there is also a family of non - isotropic equilibria. we give a rigorous prove of convergence of the solution to a steady - state as time goes to infinity. in particular we show that in the supercritical case, the only initial conditions leading to the uniform distribution in large time are those with vanishing momentum. for any positive value of the noise parameter, and any initial condition, we give rates of convergence towards equilibrium, exponentially for both supercritical and subcritical cases and algebraically for the critical case.
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arxiv:1101.2380
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expansion in some direction.
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arxiv:2301.02000
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$ \ omega _ m = 0. 35 \ pm0. 09 $.
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arxiv:astro-ph/9909205
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the \ textit { kite graph }, denoted by $ kite _ { p, q } $ is obtained by appending a complete graph $ k _ { p } $ to a pendant vertex of a path $ p _ { q } $. in this paper, firstly we show that no two non - isomorphic kite graphs are cospectral w. r. t adjacency matrix. let $ g $ be a graph which is cospectral with $ kite _ { p, q } $ and the clique number of $ g $ is denoted by $ w ( g ) $. then, it is shown that $ w ( g ) \ geq p - 2q + 1 $. also, we prove that $ kite _ { p, 2 } $ graphs are determined by their adjacency spectrum.
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arxiv:1506.01632
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we investigate the row sum of the binary pattern generated by the sierpinski automaton : interpreted as a time series we calculate the power spectrum of this sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1. 15. despite the simplicity of the model, it can serve as a model for $ 1 / f ^ \ alpha $ spectra in a certain class of experimental and natural systems like catalytic reactions and mollusc patterns.
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arxiv:cond-mat/0308277
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english is the most widely spoken language in the world, used daily by millions of people as a first or second language in many different contexts. as a result, there are many varieties of english. although the great many advances in english automatic speech recognition ( asr ) over the past decades, results are usually reported based on test datasets which fail to represent the diversity of english as spoken today around the globe. we present the first release of the edinburgh international accents of english corpus ( edacc ). this dataset attempts to better represent the wide diversity of english, encompassing almost 40 hours of dyadic video call conversations between friends. unlike other datasets, edacc includes a wide range of first and second - language varieties of english and a linguistic background profile of each speaker. results on latest public, and commercial models show that edacc highlights shortcomings of current english asr models. the best performing model, trained on 680 thousand hours of transcribed data, obtains an average of 19. 7 % word error rate ( wer ) - - in contrast to the 2. 7 % wer obtained when evaluated on us english clean read speech. across all models, we observe a drop in performance on indian, jamaican, and nigerian english speakers. recordings, linguistic backgrounds, data statement, and evaluation scripts are released on our website ( https : / / groups. inf. ed. ac. uk / edacc / ) under cc - by - sa license.
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arxiv:2303.18110
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we point out that the standard chromomagnetic penguin dipole operator has a counterpart corresponding to off - shell momenta for external quarks. by employing the chiral quark model, we show that this new dipole penguin operator has the same bosonisation as the standard q _ 6 operator. accordingly, this new operator enlarges by ~ 5 % the referent q _ 6 contribution, which gives the dominant contribution to the cp - violating ratio epsilon ' / epsilon and also gives an important contribution to the delta i = 1 / 2 amplitude.
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arxiv:0803.2106
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conjunction assessment requires knowledge of the uncertainty in the predicted orbit. errors in the atmospheric density are a major source of error in the prediction of low earth orbits. therefore, accurate estimation of the density and quantification of the uncertainty in the density is required. most atmospheric density models, however, do not provide an estimate of the uncertainty in the density. in this work, we present a new approach to quantify uncertainties in the density and to include these for calculating the probability of collision pc. for this, we employ a recently developed dynamic reduced - order density model that enables efficient prediction of the thermospheric density. first, the model is used to obtain accurate estimates of the density and of the uncertainty in the estimates. second, the density uncertainties are propagated forward simultaneously with orbit propagation to include the density uncertainties for pc calculation. for this, we account for the effect of cross - correlation in position uncertainties due to density errors on the pc. finally, the effect of density uncertainties and cross - correlation on the pc is assessed. the presented approach provides the distinctive capability to quantify the uncertainty in atmospheric density and to include this uncertainty for conjunction assessment while taking into account the dependence of the density errors on location and time. in addition, the results show that it is important to consider the effect of cross - correlation on the pc, because ignoring this effect can result in severe underestimation of the collision probability.
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arxiv:1912.01069
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detection of change - points in a sequence of high - dimensional observations is a very challenging problem, and this becomes even more challenging when the sample size ( i. e., the sequence length ) is small. in this article, we propose some change - point detection methods based on clustering, which can be conveniently used in such high dimension, low sample size situations. first, we consider the single change - point problem. using k - means clustering based on some suitable dissimilarity measures, we propose some methods for testing the existence of a change - point and estimating its location. high - dimensional behavior of these proposed methods are investigated under appropriate regularity conditions. next, we extend our methods for detection of multiple change - points. we carry out extensive numerical studies to compare the performance of our proposed methods with some state - of - the - art methods.
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arxiv:2111.14012
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a method to achieve high - brightness self - amplified spontaneous emission ( hb - sase ) in the free electron laser ( fel ) is described. the method uses repeated non - equal electron beam delays to de - localise the collective fel interaction and break the radiation coherence length dependence on the fel cooperation length. the method requires no external seeding or photon optics and so is applicable at any wavelength or repetition rate. it is demonstrated using linear theory and numerical simulations that the radiation coherence length can be increased by approximately two orders of magnitude over sase with a corresponding increase in spectral brightness. examples are shown of hb - sase generating transform - limited fel pulses in the soft x - ray and near transform - limited pulses in the hard x - ray. such pulses may greatly benefit existing applications and may also open up new areas of scientific research.
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arxiv:1212.5816
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the work is about homogenization for a type of multivalued dirichlet - neumann problems. first, we prove an average principle for general multivalued stochastic differential equations in the weak sense. then for general forward - backward coupled multivalued stochastic systems, the other average principle is presented. finally, we apply the result to a type of multivalued dirichlet - neumann problems and investigate its homogenization.
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arxiv:2406.00564
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the multiplicity schwartz - zippel lemma bounds the total multiplicity of zeroes of a multivariate polynomial on a product set. this lemma motivates the multiplicity codes of kopparty, saraf and yekhanin [ j. acm, 2014 ], who showed how to use this lemma to construct high - rate locally - decodable codes. however, the algorithmic results about these codes crucially rely on the fact that the polynomials are evaluated on a vector space and not an arbitrary product set. in this work, we show how to decode multivariate multiplicity codes of large multiplicities in polynomial time over finite product sets ( over fields of large characteristic and zero characteristic ). previously such decoding algorithms were not known even for a positive fraction of errors. in contrast, our work goes all the way to the distance of the code and in particular exceeds both the unique decoding bound and the johnson bound. for errors exceeding the johnson bound, even combinatorial list - decodablity of these codes was not known. our algorithm is an application of the classical polynomial method directly to the multivariate setting. in particular, we do not rely on a reduction from the multivariate to the univariate case as is typical of many of the existing results on decoding codes based on multivariate polynomials. however, a vanilla application of the polynomial method in the multivariate setting does not yield a polynomial upper bound on the list size. we obtain a polynomial bound on the list size by taking an alternative view of multivariate multiplicity codes. in this view, we glue all the partial derivatives of the same order together using a fresh set $ z $ of variables. we then apply the polynomial method by viewing this as a problem over the field $ \ mathbb { f } ( z ) $ of rational functions in $ z $.
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arxiv:2012.01530
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for any intrinsic gromov hyperbolic space we establish a gehring - hayman type theorem for conformally deformed spaces. as an application, we prove that any complete intrinsic hyperbolic space with atleast two points in the gromov boundary can be uniformized by densities induced by busemann functions. furthermore, we establish that there exists a natural identification of the gromov boundary of $ x $ with the metric boundary of the deformed space.
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arxiv:2408.01412
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we study a new version of the one - dimensional spin - orbital model with spins s = 1 relevant to cubic vanadates. at small hund ' s coupling j _ h we discover dimerization in a pure electronic system solely due to a dynamical spin - orbital coupling. above a critical value j _ h, a uniform ferromagnetic state is stabilized at zero temperature. more surprisingly, we observe a temperature driven dimerization of the ferrochain, which occurs due to a large entropy released by dimer states. this dynamical dimerization seems to be the mechanism driving the peculiar intermediate phase of yvo _ 3.
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arxiv:cond-mat/0212368
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many kinase inhibitors have been approved as cancer therapies. recently, libraries of kinase inhibitors have been extensively profiled, thus providing a map of the strength of action of each compound on a large number of its targets. these profiled libraries define drug - kinase networks that can predict the effectiveness of new untested drugs and elucidate the role played by specific kinases in different cellular systems. predictions of drug effectiveness based on a comprehensive network model of cellular signalling are difficult, due to our partial knowledge of the complex biological processes downstream of the targeted kinases. we have developed the kinase inhibitors elastic net ( kien ) method, which integrates information contained in drug - kinase networks with in vitro screening. the method uses the in vitro cell response of single drugs and drug pair combinations as a training set to build linear and nonlinear regression models. besides predicting the effectiveness of untested drugs, the method identifies sets of kinases that are statistically associated to drug sensitivity in a given cell line. we compare different versions of the method, which is based on a regression technique known as elastic net. data from two - drug combinations leads to predictive models, and predictivity can be improved by applying logarithmic transformation to the data. the method is applied to the a549 lung cancer cell line. a pathway enrichment analysis of the set of kinases identified by the method shows that axon guidance, activation of rac, and semaphorin interactions pathways are associated to a selective response to therapeutic intervention in this cell line.
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arxiv:1307.4802
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working toward a model independent understanding of cosmic microwave background ( cmb ) anisotropies and their significance, we undertake a comprehensive and self - contained study of scalar perturbation theory. initial conditions, evolution, thermal history, matter content, background dynamics, and geometry all play a role in determining the anisotropy. by employing { \ it analytic } techniques to illuminate the numerical results, we are able to separate and identify each contribution. we thus bring out the nature of the { \ it total } sachs - wolfe effect, acoustic oscillations, diffusion damping, doppler shifts, and reionization, as well as their particular manifestation in a critical, curvature, or cosmological constant dominated universe. by studying the full angular { \ it and } spatial content of the resultant anisotropies, we isolate the signature of these effects from the dependence on initial conditions. whereas structure in the sachs - wolfe anisotropy depends strongly on the underlying power spectra, the acoustic oscillations provide features which are nearly model independent. this may allow for future determination of the matter content of the universe as well as the adiabatic and / or isocurvature nature of the initial fluctuations.
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arxiv:astro-ph/9411008
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we present the most extensive catalog of exposures of volatiles on the 67p / churyumov - gerasimenko nucleus generated from observations acquired with the osiris cameras on board the rosetta mission. we identified more than 600 volatile exposures on the comet. bright spots are found isolated on the nucleus or grouped in clusters, usually at the bottom of cliffs, and most of them are small, typically a few square meters or smaller. several of them are clearly correlated with the cometary activity. we note a number of peculiar exposures of volatiles with negative spectral slope values in the high - resolution post - perihelion images, which we interpret as the presence of large ice grains ( $ > $ 1000 $ \ mu $ m ) or local frosts condensation. we observe a clear difference both in the spectral slope and in the area distributions of the bright spots pre - and post - perihelion, with these last having lower average spectral slope values and a smaller size, with a median surface of 0. 7 m $ ^ 2 $, even if the size difference is mainly due to the higher resolution achieved post - perihelion. the minimum duration of the bright spots shows three clusters : an area - independent cluster dominated by short - lifetime frosts ; an area - independent cluster with lifetime of 0. 5 - - 2 days, probably associated with the seasonal fallout of dehydrated chunks ; and an area - dependent cluster with lifetime longer than 2 days consistent with water - driven erosion of the nucleus. even if numerous bright spots are detected, the total surface of exposed water ice is less than 0. 1 % of the total 67p nucleus surface, confirming that the 67p surface is dominated by refractory dark terrains, while exposed ice occupies only a tiny fraction. moreover, the abundance of volatile exposures is six times less in the small lobe than in the big lobe, adding additional evidence to the hypothesis that comet 67p is composed of two distinct bodies.
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arxiv:2302.11424
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quantum state sharing ( qss ) is a protocol by which a ( secret ) quantum state may be securely split, shared between multiple potentially dishonest players, and reconstructed. crucially the players are each assumed to be dishonest, and so qss requires that only a collaborating authorised subset of players can access the original secret state ; any dishonest unauthorised conspiracy cannot reconstruct it. we analyse a qss protocol involving three untrusted players and demonstrate that quantum steering is the required resource which enables the protocol to proceed securely. we analyse the level of steering required to share any single - mode gaussian secret which enables the states to be shared with the optimal use of resources.
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arxiv:2106.06337
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snd @ lhc is a compact and stand - alone experiment designed to perform measurements with neutrinos produced at the lhc in the pseudo - rapidity region of $ { 7. 2 < \ eta < 8. 4 } $. the experiment is located 480 m downstream of the atlas interaction point, in the ti18 tunnel. the detector is composed of a hybrid system based on an 830 kg target made of tungsten plates, interleaved with emulsion and electronic trackers, also acting as an electromagnetic calorimeter, and followed by a hadronic calorimeter and a muon identification system. the detector is able to distinguish interactions of all three neutrino flavours, which allows probing the physics of heavy flavour production at the lhc in the very forward region. this region is of particular interest for future circular colliders and for very high energy astrophysical neutrino experiments. the detector is also able to search for the scattering of feebly interacting particles. in its first phase, the detector will operate throughout lhc run 3 and collect a total of 250 $ \ text { fb } ^ { - 1 } $.
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arxiv:2210.02784
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let $ a $ be an algebraically simple, separable, nuclear, $ \ mathcal { z } $ - stable $ c ^ * $ - algebra for which the trace space $ t ( a ) $ is a bauer simplex and the extremal boundary $ \ partial _ e t ( a ) $ has finite covering dimension. we prove that each automorphism $ \ alpha $ on $ a $ is cocycle conjugate to its tensor product with the trivial automorphism on the jiang - su algebra. at least for single automorphisms this generalizes a recent result by gardella - hirshberg - vaccaro. if $ \ alpha $ is strongly outer as an action of $ \ mathbb { z } $, we prove it has finite rokhlin dimension with commuting towers. as a consequence it tensorially absorbs any automorphism on the jiang - su algebra.
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arxiv:2105.04469
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we describe the design, construction and operation of the askaryan radio array ( ara ) autonomous renewable power stations, initially installed at the south pole in december, 2010 with the goal of providing an independently operating 100 w power source capable of year - round operation in extreme environments. in addition to particle astrophysics applications at the south pole, such a station can easily be, and has since been, extended to operation elsewhere, as described herein.
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arxiv:1403.1253
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code voting was introduced by chaum as a solution for using a possibly infected - by - malware device to cast a vote in an electronic voting application. chaum ' s work on code voting assumed voting codes are physically delivered to voters using the mail system, implicitly requiring to trust the mail system. this is not necessarily a valid assumption to make - especially if the mail system cannot be trusted. when conspiring with the recipient of the cast ballots, privacy is broken. it is clear to the public that when it comes to privacy, computers and " secure " communication over the internet cannot fully be trusted. this emphasizes the importance of using : ( 1 ) unconditional security for secure network communication. ( 2 ) reduce reliance on untrusted computers. in this paper we explore how to remove the mail system trust assumption in code voting. we use psmt protocols ( scn 2012 ) where with the help of visual aids, humans can carry out $ \ mod 10 $ addition correctly with a 99 \ % degree of accuracy. we introduce an unconditionally secure mix based on the combinatorics of set systems. given that end users of our proposed voting scheme construction are humans we \ emph { cannot use } classical secure multi party computation protocols. our solutions are for both single and multi - seat elections achieving : \ begin { enumerate } [ i ) ] \ item an anonymous and perfectly secure communication network secure against a $ t $ - bounded passive adversary used to deliver voting, \ item the end step of the protocol can be handled by a human to evade the threat of malware. \ end { enumerate } we do not focus on active adversaries.
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arxiv:1506.04429
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the battle for a more secure internet is waged on many fronts, including the most basic of networking protocols. our focus is the ipv4 identifier ( ipid ), an ipv4 header field as old as the internet with an equally long history as an exploited side channel for scanning network properties, inferring off - path connections, and poisoning dns caches. this article taxonomizes the 25 - year history of ipid - based exploits and the corresponding changes to ipid selection methods. by mathematically analyzing these methods ' correctness and security and empirically evaluating their performance, we reveal recommendations for best practice as well as shortcomings of current operating system implementations, emphasizing the value of systematic evaluations in network security.
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arxiv:2406.06483
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a toric degeneration of an irreducible variety is a flat degeneration to an irreducible toric variety. in the case of a flag variety, its toric degeneration with desirable properties induces degenerations of richardson varieties to unions of irreducible closed toric subvarieties, called semi - toric degenerations. for instance, morier - genoud proved that caldero ' s toric degenerations arising from string polytopes have this property. semi - toric degenerations are closely related to schubert calculus. indeed, kogan - miller constructed semi - toric degenerations of schubert varieties from knutson - miller ' s semi - toric degenerations of matrix schubert varieties which give a geometric proof of the pipe dream formula of schubert polynomials. in this paper, we focus on a toric degeneration of a flag variety arising from a cluster structure, and prove that it induces semi - toric degenerations of richardson varieties. our semi - toric degeneration can be regarded as a generalization of morier - genoud ' s and kogan - miller ' s semi - toric degenerations.
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arxiv:2110.12731
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a custom, flat field, extreme ultraviolet euv spectrometer built specifically for use with low power light sources that operate under ultrahigh vacuum conditions is reported. the spectral range of the spectrometer extends from 4 nm to 40 nm. the instrument optimizes the light gathering power and signal to noise ratio while achieving good resolution. a detailed description of the spectrometer and design considerations are presented, as well as a novel procedure that could be used to obtain a synthetic wavelength calibration with the aid of only a single known spectral feature. this synthetic wavelength calibration is compared to a standard wavelength calibration obtained from previously reported spectral lines of xe, ar and ne ions recorded with this spectrometer.
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arxiv:physics/0508048
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we consider a randomization of a function on $ \ mathbb r ^ d $ that is naturally associated to the wiener decomposition and, intrinsically, to the modulation spaces. such randomized functions enjoy better integrability, thus allowing us to improve the strichartz estimates for the schr \ " odinger equation. as an example, we also show that the energy - critical cubic nonlinear schr \ " odinger equation on $ \ mathbb r ^ 4 $ is almost surely locally well - posed with respect to randomized initial data below the energy space.
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arxiv:1405.7326
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in the context of inferring a bayesian network structure ( directed acyclic graph, dag for short ), we devise a non - reversible continuous time markov chain, the ` ` causal zig - zag sampler ' ', that targets a probability distribution over classes of observationally equivalent ( markov equivalent ) dags. the classes are represented as completed partially directed acyclic graphs ( cpdags ). the non - reversible markov chain relies on the operators used in chickering ' s greedy equivalence search ( ges ) and is endowed with a momentum variable, which improves mixing significantly as we show empirically. the possible target distributions include posterior distributions based on a prior over dags and a markov equivalent likelihood. we offer an efficient implementation wherein we develop new algorithms for listing, counting, uniformly sampling, and applying possible moves of the ges operators, all of which significantly improve upon the state - of - the - art run - time.
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arxiv:2310.05655
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we develop a high - order kinetic scheme for entropy - based moment models of a one - dimensional linear kinetic equation in slab geometry. high - order spatial reconstructions are achieved using the weighted essentially non - oscillatory ( weno ) method, and for time integration we use multi - step runge - kutta methods which are strong stability preserving and whose stages and steps can be written as convex combinations of forward euler steps. we show that the moment vectors stay in the realizable set using these time integrators along with a maximum principle - based kinetic - level limiter, which simultaneously dampens spurious oscillations in the numerical solutions. we present numerical results both on a manufactured solution, where we perform convergence tests showing our scheme converges of the expected order up to the numerical noise from the numerical optimization, as well as on two standard benchmark problems, where we show some of the advantages of high - order solutions and the role of the key parameter in the limiter.
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arxiv:1501.07765
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a distant, massive planet in the outer solar system has recently been proposed to explain some observed features of extreme trans - neptunian objects ( tnos ). here we use n - body simulations of the formation of the kuiper belt and oort cloud as well as a survey simulator to compare models of the solar system with and without a 9th planet to one another as well as to observations. the main mechanism for tnos to be deposited into the distant ( $ a $ > au ), detached ( $ q $ > au ) region of the kuiper belt in the 8 - planet model is kozai - lidov oscillation of objects in mean motion resonances ( mmr ) with neptune. this effect does not deposit low - inclination ( $ i \ lesssim $ 20 { \ deg } ) objects into this region. however, we find that the 9th planet generates a group of distant, detached tnos at low inclinations that are not present in the 8 - planet model. this disparity between the 8 - planet and the 9 - planet models could provide a strong constraint on a possible planet 9 with further detections of tnos in the distant, detached region of the kuiper belt.
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arxiv:2109.13307
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we propose a novel bound on the mimimum dissipation required in any circumstances to transfer a certain amount of charge through any resistive device. we illustrate it on the task of writing a logical 1 ( encoded as a prescribed voltage ) into a capacitance, through various linear or nonlinear devices. we show that, even though the celebrated landauer bound ( which only applies to bit erasure ) does not apply here, one can still formulate a " non - landauer " lower bound on dissipation, that crucially depends on the time budget to perform the operation, as well as the average conductance of the driving device. we compare our bound with empirical results reported in the literature and realistic simulations of cmos pass and transmission gates in decananometer technology. our non - landauer bound turns out to be a quantitative benchmark to assess the ( non - ) optimality of a writing operation.
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arxiv:2307.08993
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biased sampling methods such as the temperature accelerated sliced sampling ( tass ), which can explore high dimensional collective variable ( cv ) space, is of great interest in free energy calculations. such methods can efficiently sample configurational space even when a large number of cvs for biasing are used while many conventional methods are limited to two or three cvs. in this paper, we propose a modification to the tass method, called parallel bias tass or pbtass, wherein a multidimensional parallel metadynamics bias is incorporated on a selected set of cvs. the corresponding time - dependent reweighting equations are derived, and the method is benchmarked. in particular, we compare the accuracy and efficiency of pbtass with various methods viz. standard tass, temperature accelerated molecular dynamics / driven - adiabatic free energy dynamics, and parallel bias metadynamics. we demonstrate the capability of the pbtass method by reconstructing the eight - dimensional free energy surface of alanine pentapeptide in vacuo from a 25 ns long trajectory. free energy barriers and free energies of high energy saddle points on the high dimensional free energy landscape of this system are reported.
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arxiv:2010.01646
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we present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. previously we consistently derived special relativistic hydrodynamic equations with weak gravity in minkowski background. with the relativistic pressure and velocity one cannot derive the cosmological counterpart by a simple transformation from equations in the minkowski background. here we present a proper derivation. we point out the potential importance of relativistic pressure and velocity in gravitational lensing.
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arxiv:1809.01182
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we present a method for obtaining congruences modulo powers of 3 for sequences given by recurrences of finite depth with polynomial coefficients. we apply this method to catalan numbers, motzkin numbers, riordan numbers, schr \ " oder numbers, eulerian numbers, trinomial coefficients, delannoy numbers, and to functions counting free subgroups of finite index in the inhomogeneous modular group and its lifts. this leads to numerous new results, including many extensions of known results to higher powers of 3.
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arxiv:1308.2856
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we interpret penumbral filaments as due to convection in field - free, radially aligned gaps just below the visible surface of the penumbra, intruding into a nearly potential field above. this solves the classical discrepancy between the large heat flux and the low vertical velocities observed in the penumbra. the presence of the gaps causes strong small - scale fluctuations in inclination, azimuth angle and field strength, but without strong forces acting on the gas. the field is nearly horizontal in a region around the cusp - shaped top of the gap, thereby providing an environment for evershed flows. we identify this region with the recently discovered dark penumbral cores. its darkness has the same cause as the dark lanes in umbral light - bridges, reproduced in numerical simulations by nordlund and stein ( 2005 ). we predict that the large vertical and horizontal gradients of the magnetic field inclination and azimuth in the potential field model will produce the net circular polarization seen in observations. the model also explains the significant elevation of bright filaments above their surroundings. it predicts that dark areas in the penumbra are of two different kinds : dark filament cores containing the most inclined ( horizontal ) fields, and regions between bright filaments, containing the least inclined field lines.
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arxiv:astro-ph/0508504
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i attempt to experimentally evaluate the prospects of synthesizing new neutron - rich superheavy nuclei. i consider three possible synthetic paths to neutron - rich superheavy nuclei : ( a ) the use of neutron - rich radioactive beams. ( b ) the use of damped collisions and ( c ) the use of multi - nucleon transfer reactions. i consider the prospects of synthesizing new n - rich isotopes of rf - bh using light n - rich radioactive beams and targeted beams from rea3, frib and spiral2. for the damped collision path, i present the results of a study of a surrogate reaction, 160gd + 186w. these data indicate the formation of au ( trans - target ) fragments and the depletion of yields of target - like fragments by fission and fragment emission. the data are compared to predictions of zagrebaev and greiner. for the multi - nucleon transfer reactions, the results of a study of the 136xe + 208pb reaction are discussed. i consider the possibility of multi - nucleon transfer reactions with radioactive beams.
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arxiv:1301.1759
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we define filtered adhm data and connect a notion of filtered quiver representations to grothendieck - - springer resolutions. we also provide current developments and give a list of research problems to further study filtered adhm equation.
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arxiv:1912.10191
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we measured electron energy distribution functions ( eedfs ) from below 200 ev to over 8 kev and spanning five orders - of - magnitude in intensity, produced in a low - power, rf - heated, tandem mirror discharge in the pfrc - ii apparatus. the eedf was obtained from the x - ray energy distribution function ( xedf ) using a novel poisson - regularized spectrum inversion algorithm applied to pulse - height spectra that included both bremsstrahlung and line emissions. the xedf was measured using a specially calibrated amptek silicon drift detector ( sdd ) pulse - height system with 125 ev fwhm at 5. 9 kev.
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arxiv:1712.05422
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a classical result by solodov states that if a group acts on the line such that any non - trivial element has at most one fixed point, then the action is either abelian or semi - conjugate to an affine action. we show that the same holds if we relax the assumption, requiring that any non - trivial element has at most 2 fixed points.
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arxiv:2210.07616
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the method of stable random projections is popular for efficiently computing the lp distances in high dimension ( where 0 < p < = 2 ), using small space. because it adopts nonadaptive linear projections, this method is naturally suitable when the data are collected in a dynamic streaming fashion ( i. e., turnstile data streams ). in this paper, we propose to use only the signs of the projected data and analyze the probability of collision ( i. e., when the two signs differ ). we derive a bound of the collision probability which is exact when p = 2 and becomes less sharp when p moves away from 2. interestingly, when p = 1 ( i. e., cauchy random projections ), we show that the probability of collision can be accurately approximated as functions of the chi - square similarity. for example, when the ( un - normalized ) data are binary, the maximum approximation error of the collision probability is smaller than 0. 0192. in text and vision applications, the chi - square similarity is a popular measure for nonnegative data when the features are generated from histograms. our experiments confirm that the proposed method is promising for large - scale learning applications.
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arxiv:1308.1009
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we investigate theoretically the non - linear dynamics of a coupled nanomechanical oscillator. under a weak radio frequency excitation, the resonators can be parametrically tuned into a self - sustained oscillatory regime. the transfer of electrons from one contact to the other is then mechanically assisted, generating a rectified current. the direction of the rectified current is, in most unstable regions, determined by the phase shift between the mechanical oscillations and the signal. however, we locate intriguing parametrical regions of uni - directional rectified current, suggesting a practical scheme for the realization of a self - powered device in the nanoscale. in these regions, a dynamical symmetry breaking is induced by the non - linear coupling of the mechanical and electrical degrees of freedom. when operating within the coulomb blockade limit, we locate bands of instability of enhanced gain.
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arxiv:1307.7576
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we study a natural class of fermi - ulam models that features good hyperbolicity properties and that we call dispersing fermi - ulam models. using tools inspired by the theory of hyperbolic billiards we prove, under very mild complexity assumptions, a growth lemma for our systems. this allows us to obtain ergodicity of dispersing fermi - ulam models. it follows that almost every orbit of such systems is oscillatory.
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arxiv:2003.00053
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the minimal supersymmetric ( susy ) standard model ( mssm ) augmented by right chiral sneutrinos may lead to one such sneutrino serving as the lightest supersymmetric particle and a non - thermal dark matter candidate, especially if neutrinos have dirac masses only. in such cases, if the lightest mssm particle is a stau, the signal of susy at the lhc consists in stable charged tracks which are distinguishable from backgrounds through their time delay between the inner tracker and the muon chamber. we show how to determine in such scenarios the mass hierarchy between the lightest neutralino and right sleptons of the first two families. the techniques of neutralino reconstruction, developed in earlier works, are combined with the endpoint of the variable $ m _ { t2 } $ in smuon ( selectron ) decays for this purpose. we show that one can thus determine the mass hierarchy for smuons ( selectrons ) and neutralinos up to 1 tev, to the level of 5 - 10 \ %.
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arxiv:1806.04488
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sampling strategies are important for sparse imaging methodologies, especially those employing the discrete fourier transform ( dft ). chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with finite, iterative reconstruction schemes to form an image from limited samples. using a sampling pattern constructed entirely from periodic lines in dft space, chaotic sensing was found to outperform traditional compressed sensing for magnetic resonance imaging ; however, only one such sampling pattern was presented and the reason for its fractal nature was not proven. through the introduction of a novel image transform known as the kaleidoscope transform, which formalises and extends upon the concept of downsampling and concatenating an image with itself, this paper : ( 1 ) demonstrates a fundamental relationship between multiplication in modular arithmetic and downsampling ; ( 2 ) provides a rigorous mathematical explanation for the fractal nature of the sampling pattern in the dft ; and ( 3 ) leverages this understanding to develop a collection of novel fractal sampling patterns for the 2d dft with customisable properties. the ability to design tailor - made fractal sampling patterns expands the utility of the dft in chaotic imaging and may form the basis for a bespoke chaotic sensing methodology, in which the fractal sampling matches the imaging task for improved reconstruction.
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arxiv:2108.00639
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vhs j1256 $ - $ 1257 ab is an ultracool dwarf binary that hosts a wide - separation planetary - mass companion that is a key target of the { \ sl jwst } exoplanet early release science ( ers ) program. using keck adaptive optics imaging and aperture masking interferometry, we have determined the host binary ' s orbit, $ a = 1. 96 \ pm0. 03 $ au, $ p = 7. 31 \ pm0. 02 $ yr, $ e = 0. 883 \ pm0. 003 $, and measured its dynamical total mass, $ 0. 141 \ pm0. 008 $ $ m _ { \ odot } $. this total mass is consistent with vhs j1256 $ - $ 1257 ab being a brown dwarf binary or pair of very low - mass stars. in addition, we measured the orbital motion of vhs j1256 $ - $ 1257 b with respect to the barycenter of vhs j1256 $ - $ 1257 ab, finding that the wide companion ' s orbit is also eccentric, $ e = 0. 68 ^ { + 0. 11 } _ { - 0. 10 } $, with a mutual inclination of $ 115 \ pm14 ^ { \ circ } $ with respect to the central binary. this orbital architecture is consistent with vhs j1256 $ - $ 1257 b attaining a significant mutual inclination through dynamical scattering and thereafter driving kozai - lidov cycles to pump the eccentricity of vhs j1256 $ - $ 1257 ab. we derive a cooling age of $ 140 \ pm20 $ myr for vhs j1256 $ - $ 1257 ab from low - mass stellar / substellar evolutionary models. at this age, the luminosity of vhs j1256 $ - $ 1257 b is consistent with both deuterium - inert and deuterium - fusing evolutionary tracks. we thus find a bimodal probability distribution for the mass of vhs j1256 $ - $ 1257 b, either $ 12. 0 \ pm0. 1 $ $ m _ { \ rm jup } $ or $ 16 \ pm1 $ $ m _ { \ rm jup } $, from these models. future spectroscopic data to measure isotopologues such as hdo and ch $ _ 3 $ d could break this degeneracy and provide a strong test of substellar models at the
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arxiv:2208.08448
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the lattice technique of studying the strong interaction of matter is used to obtain predictions of the hadronic spectrum. these simulations were performed by the ukqcd collaboration using full ( unquenched ) qcd. details of the results, a comparison with quenched data, and novel methods of extracting spectral properties are described.
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arxiv:hep-lat/0012026
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context : the success of stack overflow and other community - based question - and - answer ( q & a ) sites depends mainly on the will of their members to answer others ' questions. in fact, when formulating requests on q & a sites, we are not simply seeking for information. instead, we are also asking for other people ' s help and feedback. understanding the dynamics of the participation in q & a communities is essential to improve the value of crowdsourced knowledge. objective : in this paper, we investigate how information seekers can increase the chance of eliciting a successful answer to their questions on stack overflow by focusing on the following actionable factors : affect, presentation quality, and time. method : we develop a conceptual framework of factors potentially influencing the success of questions in stack overflow. we quantitatively analyze a set of over 87k questions from the official stack overflow dump to assess the impact of actionable factors on the success of technical requests. the information seeker reputation is included as a control factor. furthermore, to understand the role played by affective states in the success of questions, we qualitatively analyze questions containing positive and negative emotions. finally, a survey is conducted to understand how stack overflow users perceive the guideline suggestions for writing questions. results : we found that regardless of user reputation, successful questions are short, contain code snippets, and do not abuse with uppercase characters. as regards affect, successful questions adopt a neutral emotional style. conclusion : we provide evidence - based guidelines for writing effective questions on stack overflow that software engineers can follow to increase the chance of getting technical help. as for the role of affect, we empirically confirmed community guidelines that suggest avoiding rudeness in question writing.
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arxiv:1710.04692
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millimeter wave beam alignment ( ba ) is a challenging problem especially for large number of antennas. compressed sensing ( cs ) tools have been exploited due to the sparse nature of such channels. this paper presents a novel deterministic cs approach for ba. our proposed sensing matrix which has a kronecker - based structure is sparse, which means it is computationally efficient. we show that our proposed sensing matrix satisfies the restricted isometry property ( rip ) condition, which guarantees the reconstruction of the sparse vector. our approach outperforms existing random beamforming techniques in practical low signal to noise ratio ( snr ) scenarios.
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arxiv:1909.06985
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deepseek - r1, the largest open - source mixture - of - experts ( moe ) model, has demonstrated reasoning capabilities comparable to proprietary frontier models. prior research has explored expert routing in moe models, but findings suggest that expert selection is often token - dependent rather than semantically driven. given deepseek - r1 ' s enhanced reasoning abilities, we investigate whether its routing mechanism exhibits greater semantic specialization than previous moe models. to explore this, we conduct two key experiments : ( 1 ) a word sense disambiguation task, where we examine expert activation patterns for words with differing senses, and ( 2 ) a cognitive reasoning analysis, where we assess deepseek - r1 ' s structured thought process in an interactive task setting of discoveryworld. we conclude that deepseek - r1 ' s routing mechanism is more semantically aware and it engages in structured cognitive processes.
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arxiv:2502.10928
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a light field camera can reconstruct 3d scenes using captured multi - focus images that contain rich spatial geometric information, enhancing applications in stereoscopic photography, virtual reality, and robotic vision. in this work, a state - of - the - art salient object detection model for multi - focus light field images, called lfsamba, is introduced to emphasize four main insights : ( a ) efficient feature extraction, where sam is used to extract modality - aware discriminative features ; ( b ) inter - slice relation modeling, leveraging mamba to capture long - range dependencies across multiple focal slices, thus extracting implicit depth cues ; ( c ) inter - modal relation modeling, utilizing mamba to integrate all - focus and multi - focus images, enabling mutual enhancement ; ( d ) weakly supervised learning capability, developing a scribble annotation dataset from an existing pixel - level mask dataset, establishing the first scribble - supervised baseline for light field salient object detection. https : / / github. com / liuzywen / lfscribble
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arxiv:2411.06652
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in this paper we study the evolution of multiple fluids with different constant densities in porous media. this physical scenario is known as the muskat and the ( multi - phase ) hele - shaw problems. in this context we prove that the fluids do not develop squirt singularities.
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arxiv:0911.4109
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we consider the grover walk model on a connected finite graph with two infinite length tails and we set an $ \ ell ^ \ infty $ - infinite external source from one of the tails as the initial state. we show that for any connected internal graph, a stationary state exists, moreover a perfect transmission to the opposite tail always occurs in the long time limit. we also show that the lower bound of the norm of the stationary measure restricted to the internal graph is proportion to the number of edges of this graph. furthermore when we add more tails ( e. g., $ r $ - tails ) to the internal graph, then we find that from the temporal and spatial global view point, the scattering to each tail in the long time limit coincides with the local one - step scattering manner of the grover walk at a vertex whose degree is $ ( r + 1 ) $.
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arxiv:1812.04730
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in order to provide an estimate of eps ' / eps several effective theories and physical effects have to be disentangled. in this talk i discuss how it is possible to predict eps ' / eps taking into account all sources of large logs. the numerical result one obtains, $ \ eps ' / \ eps \ sim ( 1. 7 \ pm 0. 6 ) \ cdot 10 ^ { - 4 } $, is in good agreement with present measurements.
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arxiv:hep-ph/0011125
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one of the most challenging scenarios for smart speakers is multi - talker, when target speech from the desired speaker is mixed with interfering speech from one or more speakers. a smart assistant needs to determine which voice to recognize and which to ignore and it needs to do so in a streaming, low - latency manner. this work presents two multi - microphone speech enhancement algorithms targeted at this scenario. targeting on - device use - cases, we assume that the algorithm has access to the signal before the hotword, which is referred to as the noise context. first is the context aware beamformer which uses the noise context and detected hotword to determine how to target the desired speaker. the second is an adaptive noise cancellation algorithm called speech cleaner which trains a filter using the noise context. it is demonstrated that the two algorithms are complementary in the signal - to - noise ratio conditions under which they work well. we also propose an algorithm to select which one to use based on estimated snr. when using 3 microphone channels, the final system achieves a relative word error rate reduction of 55 % at - 12db, and 43 \ % at 12db.
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arxiv:2205.08555
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the system of four point vortices in the plane has relative equilibria that behave as composite particles, in the case where three of the vortices have strength $ - \ gamma / 3 $ and one of the vortices has strength $ \ gamma $. these relative equilibria occur at nongeneric momenta. the reduction of this system, at those momenta, by continuous and then discrete symmetries, classifies the 4 - vortex states which have been observed as products of collisions of two such composite particles. in this article i explicitly calculate these reductions, and show they are qualitatively identical one degree of freedom systems on a cylinder. the flows on these reduced systems all have one stable equilibrium and one unstable equilibrium, and all the orbits are periodic except for two homoclinic connections to the unstable equilibrium.
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arxiv:math-ph/9910012
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