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optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. since the rank constraint is non - convex, these problems are often approximately solved via convex relaxations. nuclear norm regularization is the prevailing convexifying technique for dealing with these types of problem. this paper introduces a family of low - rank inducing norms and regularizers which includes the nuclear norm as a special case. a posteriori guarantees on solving an underlying rank constrained optimization problem with these convex relaxations are provided. we evaluate the performance of the low - rank inducing norms on three matrix completion problems. in all examples, the nuclear norm heuristic is outperformed by convex relaxations based on other low - rank inducing norms. for two of the problems there exist low - rank inducing norms that succeed in recovering the partially unknown matrix, while the nuclear norm fails. these low - rank inducing norms are shown to be representable as semi - definite programs. moreover, these norms have cheaply computable proximal mappings, which makes it possible to also solve problems of large size using first - order methods. | arxiv:1612.03186 |
animals exploit time to survive in the world. temporal information is required for higher - level cognitive abilities such as planning, decision making, communication, and effective cooperation. since time is an inseparable part of cognition, there is a growing interest in the artificial intelligence approach to subjective time, which has a possibility of advancing the field. the current survey study aims to provide researchers with an interdisciplinary perspective on time perception. firstly, we introduce a brief background from the psychology and neuroscience literature, covering the characteristics and models of time perception and related abilities. secondly, we summarize the emergent computational and robotic models of time perception. a general overview to the literature reveals that a substantial amount of timing models are based on a dedicated time processing like the emergence of a clock - like mechanism from the neural network dynamics and reveal a relationship between the embodiment and time perception. we also notice that most models of timing are developed for either sensory timing ( i. e. ability to assess an interval ) or motor timing ( i. e. ability to reproduce an interval ). the number of timing models capable of retrospective timing, which is the ability to track time without paying attention, is insufficient. in this light, we discuss the possible research directions to promote interdisciplinary collaboration in the field of time perception. | arxiv:2007.11845 |
we consider binary infinite order stochastic chains perturbed by a random noise. this means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. we show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. as a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm context, provided that the noise is small enough. | arxiv:0707.2796 |
we consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the bbm, the dai ' s, the camassa - holm, and the dullin - gottwald - holm equations, as well as some recent shallow water equations with the coriolis effect. we establish unique continuation results and exhibit asymptotic profiles for the solutions of the general class considered. from these results we prove the non - existence of non - trivial spatially compactly supported solutions for the equation. as an aftermath, we study the equations earlier mentioned in light of our results for the general class. | arxiv:2212.10034 |
we study the approximate differentiability of measurable mappings of carnot - - carath \ ' eodory spaces. we show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields almost everywhere. as a geometric tool we prove the generalization of rashevsky - - chow theorem for $ c ^ 1 $ - smooth vector fields. the main result of the paper extends theorems on approximate differentiability proved by stepanoff ( 1923, 1925 ) and whitney ( 1951 ) in euclidean spaces and by vodopyanov ( 2000 ) on carnot groups. | arxiv:1206.5197 |
generalization, i. e., the ability of solving problem instances that are not available during the system design and development phase, is a critical goal for intelligent systems. a typical way to achieve good generalization is to learn a model from vast data. in the context of heuristic search, such a paradigm could be implemented as configuring the parameters of a parallel algorithm portfolio ( pap ) based on a set of training problem instances, which is often referred to as pap construction. however, compared to traditional machine learning, pap construction often suffers from the lack of training instances, and the obtained paps may fail to generalize well. this paper proposes a novel competitive co - evolution scheme, named co - evolution of parameterized search ( ceps ), as a remedy to this challenge. by co - evolving a configuration population and an instance population, ceps is capable of obtaining generalizable paps with few training instances. the advantage of ceps in improving generalization is analytically shown in this paper. two concrete algorithms, namely ceps - tsp and ceps - vrpspdtw, are presented for the traveling salesman problem ( tsp ) and the vehicle routing problem with simultaneous pickup - delivery and time windows ( vrpspdtw ), respectively. experimental results show that ceps has led to better generalization, and even managed to find new best - known solutions for some instances. | arxiv:2007.00501 |
the widespread adoption of online social networks in daily life has created a pressing need for effectively classifying user - generated content. this work presents techniques for classifying linked content spread on forum websites - - specifically, links to news articles or blogs - - using user interaction signals alone. importantly, online forums such as reddit do not have a user - generated social graph, which is assumed in social network behavioral - based classification settings. using reddit as a case - study, we show how to obtain a derived social graph, and use this graph, reddit post sequences, and comment trees as inputs to a recurrent graph neural network ( r - gnn ) encoder. we train the r - gnn on news link categorization and rumor detection, showing superior results to recent baselines. our code is made publicly available at https : / / github. com / google - research / social _ cascades. | arxiv:2108.03548 |
despite the decades of efforts, the choice of eeg reference is still a debated fundamental issue. non - neutral reference can inevitably inject the uncontrolled temporal biases into all eeg recordings, which may influence the spatiotemporal analysis of brain activity. a method, termed microstates, identifying spatiotemporal eeg features as the quasi - stable topography states in milliseconds, suggests its potential as biomarkers of neurophysiological disease. as reference electrode standardization technique ( rest ) could reconstruct an infinity reference approximately, it is a question whether rest or the other references will be more reliable than average reference ( ar ) for the microstates analysis. in this study, we design the microstate - based eeg forward model, and apply different references for microstates analysis. the spatial similarity between the generated and assumed cluster maps is mainly investigated. furthermore, the real eeg data by the parametric bootstrap method is used to validate the performance of the references. finally, we find that rest is robust to recover more similar cluster maps to the assumption than ar in the simulation, and the cluster maps between rest and ar on the real eeg data are quite different. this study may indicate that rest contributes to identifying more objective microstates features than ar. | arxiv:1802.02701 |
nuclear reaction modelling, and others. the use of data mining in discovery science follows a general trend of increasing use of computers and computational theory in all fields of science, and newer methods of data mining employ specialised machine learning algorithms for automated hypothesis forming and automated theorem proving. = = applications = = while computational methods are gaining interest, there is a decline in efforts to support critical care through basic and translational science, i. e., forms of discovery science which are essential for advancing understanding of pathophysiology. a loss of interest in basic and translational science may lead to a failure to discover and develop new therapies, which could have an impact on the critically ill. within critical care, there is an aim to renew emphasis on basic, translational science through platforms such as medical journals and conferences, as well as the critical care medical curricula. advances in discovery - based science thereby underlie key discoveries and development in medicine, constituting a ' pipeline ' for leading - edge medical development. = = = medicine = = = according to the aacr cancer progress report 2021, discovery science has the potential to drive clinical breakthroughs. since discovery science underlies key discoveries and development of new therapies for medicine, it remains important for advancing critical care. numerous discoveries have increased life span and productivity, and decreased health - related costs, thereby revolutionising medical care. resultantly, return on investment for discovery science has proven to be high. for example, its combination of computational methods with knowledge on inflammatory and genomic pathways has resulted in optimised clinical trials. ultimately, discovery science is currently enabling a transition to the era of personalised medicine for treating complex syndromes, e. g., sepsis and ards. with a robust infrastructure, discovery science can resultantly revolutionise medical care and biological research. = = = genomics = = = discovery science has converged with clinical medicine and cancer genomics, and this convergence has been accelerated by recent advances in genome technologies and genomic information. the effect of cancer genomics has been noticeable in every area of cancer research. the majority of successful applications of genomic knowledge in today ' s clinical medicine involves a wealth of knowledge which has been gathered by a broad range of research and decades of work. biological insights are required to inform drug discovery and to set a clear clinical path for development. historically, acquisition of such knowledge through functional and mechanistic studies has been uncoordinated, random, and inefficient. the process of moving from cancer | https://en.wikipedia.org/wiki/Discovery_science |
this paper is devoted to prove the s. l. singh ' s common fixed point theorem for commuting mappings in cone metric spaces. in this framework, we introduce the notions of generalized kannan con - traction, generalized zamfirescu contraction and generalized weak contraction for a pair of mappings, proving afterward their respective fixed point results. | arxiv:1008.5141 |
we present a novel class of physics - informed neural networks that is formulated based on the principles of evidential deep learning, where the model incorporates uncertainty quantification by learning parameters of a higher - order distribution. the dependent and trainable variables of the pde residual loss and data - fitting loss terms are recast as functions of the hyperparameters of an evidential prior distribution. our model is equipped with an information - theoretic regularizer that contains the kullback - leibler divergence between two inverse - gamma distributions characterizing predictive uncertainty. relative to bayesian - physics - informed - neural - networks, our framework appeared to exhibit higher sensitivity to data noise, preserve boundary conditions more faithfully and yield empirical coverage probabilities closer to nominal ones. toward examining its relevance for data mining in scientific discoveries, we demonstrate how to apply our model to inverse problems involving 1d and 2d nonlinear differential equations. | arxiv:2501.15908 |
recent experiments on nanoscale conductors coupled to microwave cavities put in prospect transport investigations of electron - photon interplay in the deep quantum regime. here we propose a pump - probe scheme to investigate the transient dynamics of individual electron - photon excitations in a double quantum dot - cavity system. excitations pumped into the system decay via charge tunneling at the double dot, probed in real time. we investigate theoretically the short - time charge transfer statistics at the dot, for periodic pumping, and show that this gives access to vacuum rabi oscillations as well as excitation dynamics in the presence of double dot dephasing and relaxation. | arxiv:1402.1351 |
the vanilla fusion methods still dominate a large percentage of mainstream audio - visual tasks. however, the effectiveness of vanilla fusion from a theoretical perspective is still worth discussing. thus, this paper reconsiders the signal fused in the multimodal case from a bionics perspective and proposes a simple, plug - and - play, attention module for vanilla fusion based on fundamental signal theory and uncertainty theory. in addition, previous work on multimodal dynamic gradient modulation still relies on decoupling the modalities. so, a decoupling - free gradient modulation scheme has been designed in conjunction with the aforementioned attention module, which has various advantages over the decoupled one. experiment results show that just a few lines of code can achieve up to 2. 0 % performance improvements to several multimodal classification methods. finally, quantitative evaluation of other fusion tasks reveals the potential for additional application scenarios. | arxiv:2312.07212 |
free groups have many applications in algebraic topology. in this paper i specifically study the finitely generated free groups by using the covering spaces and fundamental groups. by the van kampen ' s theorem, we have a famous fact that the fundamental group of a wedge sum of circles is a free group. therefore, to study free groups, we could try to figure out the covering spaces of the wedge sum of circles. and in the appendix b, i prove the nielsen - schreier theorem which i will use this to study finitely index subgroups of a finitely generated free group. | arxiv:1706.09594 |
we determine the abstract commensurator com ( f ) of thompson ' s group f and describe it in terms of piecewise linear homeomorphisms of the real line and in terms of tree pair diagrams. we show com ( f ) is not finitely generated and determine which subgroups of finite index in f are isomorphic to f. we show that the natural map from the commensurator group to the quasi - isometry group of f is injective. | arxiv:0711.0919 |
we report the precise control of tunneling magnetoresistance ( tmr ) in devices of self - assembled core / shell fe $ _ 3 $ o $ _ 4 $ / co $ _ { 1 - x } $ zn $ _ x $ fe $ _ 2 $ o $ _ 4 $ nanoparticles ( $ 0 \ leq x \ leq 1 $ ). adjusting the magnetic anisotropy through the content of co $ ^ { 2 + } $ in the shell, provides an accurate tool to control the switching field between the bistable states of the tmr. in this way, different combinations of soft / hard and hard / soft core / shell configurations can be envisaged for optimizing devices with the required magnetotransport response. | arxiv:2005.10771 |
the microcavity in the form of a liquid crystal defect layer embedded in a one - dimensional photonic crystal is considered. the microcavity mode has a tunable radiation decay rate in the vicinity of a bound state in the continuum. it is demonstrated that coupling between the microcavity mode and a tamm plasmon polariton results in hybrid tamm - microcavity modes with a tunable q factor. the measured spectral features of hybrid modes are explained in the framework of the temporal coupled mode theory. | arxiv:2306.08455 |
the weyl relations, the harmonic oscillator, the hydrogen atom, the dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. this area of research is attracting more interest due to the lattice field theories and the hypothesis of a finite space. | arxiv:quant-ph/0401077 |
motivated by cognitive radios, stochastic multi - player multi - armed bandits gained a lot of interest recently. in this class of problems, several players simultaneously pull arms and encounter a collision - with 0 reward - if some of them pull the same arm at the same time. while the cooperative case where players maximize the collective reward ( obediently following some fixed protocol ) has been mostly considered, robustness to malicious players is a crucial and challenging concern. existing approaches consider only the case of adversarial jammers whose objective is to blindly minimize the collective reward. we shall consider instead the more natural class of selfish players whose incentives are to maximize their individual rewards, potentially at the expense of the social welfare. we provide the first algorithm robust to selfish players ( a. k. a. nash equilibrium ) with a logarithmic regret, when the arm performance is observed. when collisions are also observed, grim trigger type of strategies enable some implicit communication - based algorithms and we construct robust algorithms in two different settings : the homogeneous ( with a regret comparable to the centralized optimal one ) and heterogeneous cases ( for an adapted and relevant notion of regret ). we also provide impossibility results when only the reward is observed or when arm means vary arbitrarily among players. | arxiv:2002.01197 |
when training data are collected from human annotators, the design of the annotation instrument, the instructions given to annotators, the characteristics of the annotators, and their interactions can impact training data. this study demonstrates that design choices made when creating an annotation instrument also impact the models trained on the resulting annotations. we introduce the term annotation sensitivity to refer to the impact of annotation data collection methods on the annotations themselves and on downstream model performance and predictions. we collect annotations of hate speech and offensive language in five experimental conditions of an annotation instrument, randomly assigning annotators to conditions. we then fine - tune bert models on each of the five resulting datasets and evaluate model performance on a holdout portion of each condition. we find considerable differences between the conditions for 1 ) the share of hate speech / offensive language annotations, 2 ) model performance, 3 ) model predictions, and 4 ) model learning curves. our results emphasize the crucial role played by the annotation instrument which has received little attention in the machine learning literature. we call for additional research into how and why the instrument impacts the annotations to inform the development of best practices in instrument design. | arxiv:2311.14212 |
we study partially hyperbolic sets of c1 - diffeomorphisms. for these sets there are defined the strong stable and strong unstable laminations. a lamination is called dynamically minimal when the orbit of each leaf intersects the set densely. we prove that partially hyperbolic sets having a dynamically minimal lamination have empty interior. we also study the lebesgue measure and the spectral decomposition of these sets. these results can be ap - plied to c1 - generic / robustly transitive attractors with one - dimensional center bundle. | arxiv:1703.07413 |
the status of precision electroweak data, tests of the standard model, determination of its parameters, and constraints on new physics, are surveyed. | arxiv:hep-ph/9703428 |
it is shown that the recently developed hybrid code vishnu, which couples a relativistic viscous fluid dynamical description of the quark - gluon plasma ( qgp ) with a microscopic boltzmann cascade for the late hadronic rescattering stage, yields an excellent description of charged and identified hadron spectra and elliptic flow measured in 200 a gev au + au collisions at the relativistic heavy - ion collider ( rhic ). using initial conditions that incorporate event - by - event fluctuations in the initial shape and orientation of the collision fireball and values eta / s for the specific shear viscosity of the quark - gluon plasma that were recently extracted from the measured centrality dependence of the eccentricity - scaled, p _ t - integrated charged hadron elliptic flow, we obtain universally good agreement between theory and experiment for the p _ t - spectra and differential elliptic flow v _ 2 ( p _ t ) for both pions and protons at all collision centralities. | arxiv:1101.4638 |
these notes closely correspond to a series of lectures given by the first author in toulouse, on the recent extension of the theory of ode well - posedness to abstract spaces, jointly obtained by the two authors. in the last part, we describe some further developments with respect to the theory of ( possibly degenerate ) diffusion processes, in a similar setting, contained in the second author ' s phd thesis. | arxiv:1505.05292 |
we have found the complete spectrum and eigenstates for harmonic oscillations of ideal spherical and cylindrical shells, both being infinitely thin. the spectrum of the cylindrical shell has an infinite number of goldstone modes corresponding to folding deformations. this infrared catostrophe is overcome by accounting for curvature - part of energy. | arxiv:cond-mat/0008266 |
well - graded families, extremal systems and maximum systems ( the last two in the sense of vc - theory and sauer - shelah lemma on vc - dimension ) are three important classes of set systems. this paper aims to study the notion of duality in the context of these classes of set systems and then use the obtained results for studying graphs. more specifically, we are concerned with the characterization of the finite set systems which themselves and their dual systems are both well - graded, extremal or maximum. on the way to this goal, and maybe also of independent interest, we study the structure of the well - graded families with the property that the size of the system is not much bigger than the size of its essential domain, that is, the set of elements of the domain which are shattered by the system as single element subsets. as another target of the paper, we use the above results to characterize graphs whose set systems of open or closed neighbourhoods, cliques or independent sets are well - graded, extremal or maximum. we clarify the relation of such graphs to the celebrated half - graphs. through the paper, we frequently relate our investigations to the vc - dimension of the systems. also we use one - inclusion graphs associated to set systems as an important technical tool. | arxiv:2212.08373 |
it is well known that the angles in a lattice acting on hyperbolic $ n $ - space become equidistributed. in this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. using this formula we determine, among other things, the asymptotic behavior of the density function in both the small and large variable limits. this extends earlier results by boca, pasol, popa and zaharescu and kelmer and kontorovich in dimension 2 to general dimension $ n $. our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead to effective results with explicit rates. | arxiv:1409.5683 |
essential elements of quantum theory are derived from an epistemic point of view, i. e., the viewpoint that thetheory has to do with what can be said about nature. this gives a relationship to statistical reasoning and to other areas of modelling and decision making. in particular, a quantum state can be defined from an epistemic point of view to consist of two elements : a ( maximal ) question about the value of some parameter together with the answer to that question. quantization itself can be approached from the point of view of model reduction under symmetry. | arxiv:quant-ph/0511055 |
in this paper, we evaluate a semi - autonomous brain - computer interface ( bci ) for manipulation tasks. in such system, the user controls a robotic arm through motor imagery commands. in traditional process - control bci systems, the user has to provide those commands continuously in order manipulate the effector of the robot step - by - step, which results in a tiresome process for simple tasks such as pick and replace an item from a surface. here, we take a semi - autonomous approach based on a conformal geometric algebra model that solves the inverse kinematics of the robot on the fly, then the user only has to decide on the start of the movement and the final position of the effector ( goal - selection approach ). under these conditions, we implemented pick - and - place tasks with a disk as an item and two target areas placed on the table at arbitrary positions. an artificial vision ( av ) algorithm was used to obtain the positions of the items expressed in the robot frame through images captured with a webcam. then, the av algorithm is integrated to the inverse kinematics model to perform the manipulation tasks. as proof - of - concept, different users were trained to control the pick - and - place tasks through the process - control and semi - autonomous goal - selection approaches, so that the performance of both schemes could be compared. our results show the superiority in performance of the semi - autonomous approach, as well as evidence of less mental fatigue with it. | arxiv:1910.14109 |
we propose a new performance indicator to evaluate the productivity of research institutions by their disseminated scientific papers. the new quality measure includes two principle components : the normalized impact factor of the journal in which paper was published, and the number of citations received per year since it was published. in both components, the scientific impacts are weighted by the contribution of authors from the evaluated institution. as a whole, our new metric, namely, the institutional performance score takes into account both journal based impact and articles specific impacts. we apply this new scheme to evaluate research output performance of turkish institutions specialized in astronomy and astrophysics in the period of 1998 - 2012. we discuss the implications of the new metric, and emphasize the benefits of it along with comparison to other proposed institutional performance indicators. | arxiv:1508.03713 |
active reconfigurable intelligent surface ( aris ) is a newly emerging ris technique that leverages radio frequency ( rf ) reflection amplifiers to empower phase - configurable reflection elements ( res ) in amplifying the incident signal. thereby, aris can enhance wireless communications with the strengthened aris - aided links. in this letter, we propose exploiting the signal amplification capability of aris for channel estimation, aiming to improve the estimation precision. nevertheless, the signal amplification inevitably introduces the thermal noise at the aris, which can hinder the acquisition of accurate channel state information ( csi ) with conventional channel estimation methods based on passive ris ( pris ). to address this issue, we further investigate this aris - specific channel estimation problem and propose a least - square ( ls ) based channel estimator, whose performance can be further improved with the design on aris reflection patterns at the channel training phase. based on the proposed ls channel estimator, we optimize the training reflection patterns to minimize the channel estimation error variance. extensive simulation results show that our proposed design can achieve accurate channel estimation in the presence of the aris noises. | arxiv:2311.02935 |
this letter analyzes the handover probability in a drone cellular network where the initial positions of drone base stations ( dbss ) serving a set of user equipment ( ue ) on the ground are modeled by a homogeneous poisson point process ( ppp ). inspired by the mobility model considered in the third generation partnership project ( 3gpp ) studies, we assume that all the dbss move along straight lines in random directions. we further consider two different scenarios for the dbs speeds : ( i ) same speed model ( ssm ), and ( ii ) different speed model ( dsm ). assuming nearest - neighbor association policy for the ues on the ground, we characterize the handover probability of this network for both mobility scenarios. for the ssm, we compute the exact handover probability by establishing equivalence with a single - tier terrestrial cellular network, in which the base stations ( bss ) are static while the ues are mobile. we then derive a lower bound for the handover probability in the dsm by characterizing the evolution of the spatial distribution of the dbss over time. | arxiv:2002.06493 |
the relativistic fermion - antifermion bound state vector potential of constraint theory is calculated, in perturbation theory, by means of the lippmann - schwinger type equation that relates it to the scattering amplitude. leading contributions of n - photon exchange diagrams are calculated in an approximation scheme that adapts eikonal approximation to the bound state problem. they produce terms proportional, in three - dimensional x - space, to $ ( \ alpha / r ) ^ n $. the series of leading contributions is summed. | arxiv:hep-ph/9510302 |
despite the impressive performance obtained by recent single - image hand modeling techniques, they lack the capability to capture sufficient details of the 3d hand mesh. this deficiency greatly limits their applications when high - fidelity hand modeling is required, e. g., personalized hand modeling. to address this problem, we design a frequency split network to generate 3d hand mesh using different frequency bands in a coarse - to - fine manner. to capture high - frequency personalized details, we transform the 3d mesh into the frequency domain, and propose a novel frequency decomposition loss to supervise each frequency component. by leveraging such a coarse - to - fine scheme, hand details that correspond to the higher frequency domain can be preserved. in addition, the proposed network is scalable, and can stop the inference at any resolution level to accommodate different hardware with varying computational powers. to quantitatively evaluate the performance of our method in terms of recovering personalized shape details, we introduce a new evaluation metric named mean signal - to - noise ratio ( msnr ) to measure the signal - to - noise ratio of each mesh frequency component. extensive experiments demonstrate that our approach generates fine - grained details for high - fidelity 3d hand reconstruction, and our evaluation metric is more effective for measuring mesh details compared with traditional metrics. | arxiv:2307.05541 |
as a means to support the access of massive machine - type communication devices, grant - free access and non - orthogonal multiple access ( noma ) have received great deal of attention in recent years. in the grant - free transmission, each device transmits information without the granting process so that the basestation needs to identify the active devices among all potential devices. this process, called an active user detection ( aud ), is a challenging problem in the noma - based systems since it is difficult to identify active devices from the superimposed received signal. an aim of this paper is to put forth a new type of aud based on deep neural network ( dnn ). by applying the training data in the properly designed dnn, the proposed aud scheme learns the nonlinear mapping between the received noma signal and indices of active devices. as a result, the trained dnn can handle the whole aud process, achieving an accurate detection of the active users. numerical results demonstrate that the proposed aud scheme outperforms the conventional approaches in both aud success probability and computational complexity. | arxiv:1912.11782 |
$ f ( r, t ) $ gravity is a widely used extended theory of gravity introduced in \ cite { 9 } which is a straightforward generalization of $ f ( r ) $ gravity. the action in this extended theory of gravity incorporates well motivated functional forms of the ricci scalar $ r $ and trace of energy momentum tensor $ t $. the present manuscript aims at constraining the most widely used $ f ( r, t ) $ gravity model of the form $ f ( r + 2 \ lambda t ) $ to understand its coherency and applicability in cosmology. we communicate here a novel method to find an lower bound on the model parameter $ \ lambda \ gtrsim - 1. 9 \ times 10 ^ { - 8 } $ through the equation relating the cosmological constant ( $ \ lambda $ ) and the critical density of the universe ( $ \ rho _ { cr } $ ). | arxiv:1908.06759 |
we analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. we focus on the shear and bulk viscosities and study their behavior near chiral phase transition. we model the constituent quark interactions through the nambu - - jona lasinio lagrangian. the transport coefficients are calculated within kinetic theory under relaxation time approximation including in - - medium modification of quasi - - particles dispersion relations. we quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium. considering the changes of shear and bulk viscosities along the phase boundary we discuss their sensitivity to probe the existence of the critical end point. | arxiv:0811.4708 |
ghana - s current youth unemployment rate is 19. 7 %, and the country faces a significant youth unemployment problem. while a range of youth - employment programs have been created over the years, no systematic documentation and evaluation of the impacts of these public initiatives has been undertaken. clarifying which interventions work would guide policy makers in creating strategies and programs to address the youth - employment challenge. by complementing desk reviews with qualitative data gathered from focus - group discussions and key informant interviews, we observe that most youth - employment programs implemented in ghana cover a broad spectrum that includes skills training, job placement matching, seed capital, and subsidies. duplication of initiatives, lack of coordination, and few to non - existent impact evaluations of programs are the main challenges that plague these programs. for better coordination and effective policy making, a more centralized and coordinated system is needed for program design and implementation. along the same lines, ensuring rigorous evaluation of existing youth - employment programs is necessary to provide empirical evidence of the effectiveness and efficiency of these programs. | arxiv:2311.06048 |
a key limitation of learned robot control policies is their inability to generalize outside their training data. recent works on vision - language - action models ( vlas ) have shown that the use of large, internet pre - trained vision - language models as the backbone of learned robot policies can substantially improve their robustness and generalization ability. yet, one of the most exciting capabilities of large vision - language models in other domains is their ability to reason iteratively through complex problems. can that same capability be brought into robotics to allow policies to improve performance by reasoning about a given task before acting? naive use of " chain - of - thought " ( cot ) style prompting is significantly less effective with standard vlas because of the relatively simple training examples that are available to them. additionally, purely semantic reasoning about sub - tasks, as is common in regular cot, is insufficient for robot policies that need to ground their reasoning in sensory observations and the robot state. to this end, we introduce embodied chain - of - thought reasoning ( ecot ) for vlas, in which we train vlas to perform multiple steps of reasoning about plans, sub - tasks, motions, and visually grounded features like object bounding boxes and end effector positions, before predicting the robot action. we design a scalable pipeline for generating synthetic training data for ecot on large robot datasets. we demonstrate, that ecot increases the absolute success rate of openvla, the current strongest open - source vla policy, by 28 % across challenging generalization tasks, without any additional robot training data. additionally, ecot makes it easier for humans to interpret a policy ' s failures and correct its behavior using natural language. | arxiv:2407.08693 |
we develop a general theory for three states of equilibrium of amyloid peptides : the monomer, oligomer, and fibril. we assume that the oligomeric state is a disordered micelle - like collection of a few peptide chains held together loosely by hydrophobic interactions into a spherical hydrophobic core. we assume that fibrillar amyloid chains are aligned and further stabilized by ` steric zipper ' interactions - - hydrogen bonding and steric packing, in addition to specific hydrophobic sidechain contacts. the model makes a broad set of predictions, consistent with experiments : ( i ) similar to surfactant micellization, amyloid oligomerization should increase with bulk peptide concentration. ( ii ) the onset of fibrillization limits the concentration of oligomers in the solution. ( iii ) the average fibril length \ emph { vs. } monomer concentration agrees with data on $ \ alpha $ - synuclein, ( iv ) full fibril length distributions follow those of $ \ alpha $ - synuclein, ( v ) denaturants should ` melt out ' fibrils, and ( vi ) added salt should stabilize fibrils by reducing repulsions between amyloid peptide chains. interestingly, small changes in solvent conditions can : ( a ) tip the equilibrium balance between oligomer and fibril, and ( b ) cause large changes in rates, through effects on the transition - state barrier. this model may provide useful insights into the physical processes underlying amyloid diseases. | arxiv:1007.5332 |
the rare three body decay of a higgs boson to a lepton - anti lepton pair and a photon has begun to attract attention, after the first evidence for the $ h \ to z \ gamma $ at cms and atlas, which is a sub process of $ h \ to \ ell ^ + \ ell ^ - \ gamma $. to investigate some important features of this process, we suggest that the polarized forward - backward and the photon polarization asymmetries could be useful to probe its important properties, such as the behavior of yukawa coupling, resonance, and non - resonance contributions. our analysis introduces a comprehensive framework to evaluate the aforementioned polarization - dependent observables. by analyzing the polarization effects of the final - state photon and lepton separately on forward - backward asymmetries, we demonstrate that loop - induced contributions play a significant role to investigate these asymmetries. unlike the unpolarized case, where the interference effects of resonance and non - resonance effects are minimal, we show that polarization dependent observables offer a powerful tool to analyze these features of this decay mode. furthermore, these observables can provide a handy tool for probing possible signatures of physics beyond the sm. | arxiv:2410.23685 |
we find the leading - order effect of gravitational back - reaction on cosmic strings for points near kinks and cusps. near a kink, the effect diverges as the inverse cube root of the distance to the kink, and acts in a direction transverse to the worldsheet. over time the kink is rounded off, but only regions fairly close to the kink are significantly affected. near cusps, the effect diverges inverse linearly with the distance to the cusp, and acts against the direction of the cusp motion. this results in a fractional loss of string energy that diverges logarithmically with the distance of closest approach to the cusp. | arxiv:1808.08254 |
a planar integral point set is a set of non - collinear points in plane such that for any pair of the points the euclidean distance between the points is integral. we discuss the classification of planar integral point sets and provide examples of sets that are not covered by the existent classification. | arxiv:2102.12462 |
bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. these models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time, coupled to a second equation for adaptation. spikes are emitted when the membrane potential blows up or reaches a cutoff value. the precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced, and is hard to compute accurately because of the exploding nature of the system at the spike times. we thoroughly study the precision of fixed time - step integration schemes for this type of models and demonstrate that these methods produce systematic errors that are unbounded, as the cutoff value is increased, in the evaluation of the two crucial quantities : the spike time and the value of the adaptation variable at this time. precise evaluation of these quantities therefore involve very small time steps and long simulation times. in order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare this algorithm with fixed time - step euler scheme and other more accurate simulation algorithms. | arxiv:1008.1954 |
this paper concerns the finite - time blow - up and asymptotic behaviour of solutions to nonlinear volterra integrodifferential equations. our main contribution is to determine sharp estimates on the growth rates of both explosive and nonexplosive solutions for a class of equations with nonsingular kernels under weak hypotheses on the nonlinearity. in this superlinear setting we must be content with estimates of the form $ \ lim _ { t \ to \ tau } a ( x ( t ), t ) = 1 $, where $ \ tau $ is the blow - up time if solutions are explosive or $ \ tau = \ infty $ if solutions are global. our estimates improve on the sharpness of results in the literature and we also recover well - known blow - up criteria via new methods. | arxiv:1710.07583 |
neuronal spiking exhibits an exquisite combination of modulation and robustness properties, rarely matched in artificial systems. we exploit the particular interconnection structure of conductance based models to investigate this remarkable property. we find that much of neuronal modulation and robustness can be explained by separating the total transmembrane current into three different components corresponding to the three time scales of neuronal bursting. each equivalent current aggregates many ionic contributions into an equivalent voltage - dependent conductance, which defines a key modulation parameter. plugging those equivalent feedback gains in a minimal abstract model recovers many experimental modulation scenarii as modulatory paths in elementary two - parameter charts. likewise, robustness owes to the many possible physiological realizations of a same equivalent conductance, highlighting the role of equivalent conductances as prominent targets for neuromodulation and intrinsic homeostasis. | arxiv:1311.2200 |
classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. this remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. we uncover the intrinsic connection of these areas of physics and describe them using a common symplectic hamiltonian formalism. our approach is based on a proper distinction between variables and constants, i. e. on a basic but rigorous ontology of time. we link these concept with the obvious conditions for the possibility of measurements. the derived consequences put the measurement problem of quantum mechanics and the copenhagen interpretation of the quantum mechanical wavefunction into perspective. according to our ( onto - ) logic we find that spacetime can not be fundamental. we argue that a geometric interpretation of symplectic dynamics emerges from the isomorphism between the corresponding lie algebra and the representation of a clifford algebra. within this conceptional framework we derive the dimensionality of spacetime, the form of lorentz transformations and of the lorentz force and fundamental laws of physics as the planck - einstein relation, the maxwell equations and finally the dirac equation. | arxiv:1409.5338 |
we perform direct thermovoltage measurements in a single - electron transistor, using on - chip local thermometers, both in the linear and non - linear regimes. using a model which accounts for co - tunneling, we find excellent agreement with the experimental data with no free parameters even when the temperature difference is larger than the average temperature ( far - from - linear regime ). this allows us to confirm the sensitivity of the thermovoltage on co - tunneling and to find that in the non - linear regime the temperature of the metallic island is a crucial parameter. surprisingly, the metallic island tends to overheat even at zero net charge current, resulting in a reduction of the thermovoltage. | arxiv:1812.06514 |
the quantum fourier transform offers an interesting way to perform arithmetic operations on a quantum computer. we review existing quantum fourier transform adders and multipliers and propose some modifications that extend their capabilities. among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain. | arxiv:1411.5949 |
we address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. the proposed theory, besides the operators of tarski ' s theory of reals, includes predicates for comparisons, monotonicity, convexity, and derivative of functions over bounded closed intervals or unbounded intervals. our decision algorithm is obtained by showing that satisfiable formulae of our theory admit canonical models in which functional variables are interpreted as piecewise exponential functions. these can be implicitly described within the decidable tarski ' s theory of reals. our satisfiability test generalizes previous decidability results not involving derivative operators. | arxiv:2412.16091 |
spreadsheets are used extensively in industry, often for business critical purposes. in previous work we have analyzed the information needs of spreadsheet professionals and addressed their need for support with the transition of a spreadsheet to a colleague with the generation of data flow diagrams. in this paper we describe the application of these data flow diagrams for the purpose of understanding a spreadsheet with three example cases. we furthermore suggest an additional application of the data flow diagrams : the assessment of the quality of the spreadsheet ' s design. | arxiv:1111.6895 |
we investigate the ground - state properties of polyacene in terms of an extended peierls - hubbard hamiltonian with particular emphasis on its structural instability of two types : double bonds in a " cis " pattern and those in a " trans " pattern. calculating the polarized optical conductivity spectra within and beyond the hartree - fock scheme, we reveal a striking contrast between the " cis " and " trans " configurations. the two peierls - distorted states are almost degenerate in their energetics but quite distinct in their optics. | arxiv:0812.4357 |
corruptive behaviour in politics limits economic growth, embezzles public funds, and promotes socio - economic inequality in modern democracies. we analyse well - documented political corruption scandals in brazil over the past 27 years, focusing on the dynamical structure of networks where two individuals are connected if they were involved in the same scandal. our research reveals that corruption runs in small groups that rarely comprise more than eight people, in networks that have hubs and a modular structure that encompasses more than one corruption scandal. we observe abrupt changes in the size of the largest connected component and in the degree distribution, which are due to the coalescence of different modules when new scandals come to light or when governments change. we show further that the dynamical structure of political corruption networks can be used for successfully predicting partners in future scandals. we discuss the important role of network science in detecting and mitigating political corruption. | arxiv:1801.01869 |
we present our new measurement of the cross - section for charm dimuon production in neutrino - iron interactions based upon the full statistics collected by the nomad experiment. after background subtraction we observe 15, 344 charm dimuon events, providing the largest sample currently available. the analysis exploits the large inclusive charged current sample - about $ 9 \ times 10 ^ 6 $ events after all analysis cuts - and the high resolution nomad detector to constrain the total systematic uncertainty on the ratio of charm dimuon to inclusive charged current ( cc ) cross - sections to $ \ sim 2 % $. we also perform a fit to the nomad data to extract the charm production parameters and the strange quark sea content of the nucleon within the nlo qcd approximation. we obtain a value of $ m _ c ( m _ c ) = 1. 159 \ pm0. 075 $ gev / c $ ^ 2 $ for the running mass of the charm quark in the $ \ bar { \ rm ms } $ scheme and a strange quark sea suppression factor of $ \ kappa _ s = 0. 591 \ pm 0. 019 $ at $ q ^ 2 = 20 $ gev $ ^ 2 $ / c $ ^ 2 $. | arxiv:1308.4750 |
in this paper, the robust distributed relay beamforming problem is solved using the worst case approach, where the problem solution has been involved because of the effect of uncertainty of channel knowledge on the quality of service ( qos ) constraints. it is shown that the original robust design, which is a non - convex semi - infinite problem ( sip ), can be relaxed and reformed to a semi - definite problem ( sdp ). monte - carlo simulations are presented to verify the performance improvement of our proposed robust problem over existing robust and non - robust problems in terms of transmit power and symbol error probability. | arxiv:1703.01873 |
we study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3d domain. the motion of the coupled system is driven by a uniform flow at spatial infinity, with constant dimensionless velocity $ \ lambda $. we show that if $ \ lambda $ is below a critical value, $ \ lambda _ c $ ( say ), there is a unique and stable time - independent configuration, where the body is in equilibrium and the flow is steady. we also prove that, if $ \ lambda < \ lambda _ c $, no oscillatory flow may occur. successively, we investigate possible loss of uniqueness by providing necessary and sufficient conditions for the occurrence of a steady bifurcation at some $ \ lambda _ s \ ge \ lambda _ c $. | arxiv:2406.04162 |
a proton recoil method for measuring d - t neutron energy spectra using polyethylene film and si ( au ) surface barrier detector was presented. an iteration algorithm for unfolding the recoil proton energy spectrum to the neutron energy spectrum was investigated. the response matrixes r of polyethylene film at 0 degree and 45 degree were obtained by simulating the recoil proton energy spectra from the mono - energetic neutron using mcnp code. under an assumed d - t neutron spectrum, the recoil proton spectra from polyethylene film at 0 degree and 45 degree were also simulated using mcnp code. based on the response matrixes r and the simulated recoil proton spectra at 0 degree and 45 degree, the unfolded neutron spectra were respectively obtained using the iteration algorithm, and compared with the assumed neutron spectrum. the results show that the iteration algorithm method can be applied to unfold the recoil proton energy spectrum to the neutron energy spectrum for d - t neutron energy spectra measurement using recoil proton method. | arxiv:1410.4284 |
we prove that the mazur - tate elements of an eigenform $ f $ sit inside the fitting ideals of the corresponding dual selmer groups along the cyclotomic $ \ mathbb z _ p $ - extension ( up to scaling by a single constant ). our method begins with the construction of local cohomology classes built via the $ p $ - adic local langlands correspondence. from these classes, we build algebraic analogues of the mazur - tate elements which we directly verify sit in the appropriate fitting ideals. using kato ' s euler system and explicit reciprocity laws, we prove that these algebraic elements divide the corresponding mazur - tate elements, implying our theorem. | arxiv:2210.02013 |
non - - resonant decays of charmed mesons into three pseudoscalars are analyzed in a weak gauged $ u ( 4 ) _ l \ otimes u ( 4 ) _ r $ chiral lagrangian model. the calculation is free of unknown parameters and only requires the masses of pseudoscalar mesons as hadronic inputs. when comparison with experimental data is possible we find that in some processes we have good agreement and in others we are an order of magnitude below. this may be due to the absence in our calculation of final state interactions, presumably important here, and the manifest difficulty in extracting the non - - resonant contribution from an experimental point of view. | arxiv:hep-ph/9405274 |
contrastive language - image pre - training ( clip ) models have shown promising performance on zero - shot visual recognition tasks by learning visual representations under natural language supervision. recent studies attempt the use of clip to tackle zero - shot anomaly detection by matching images with normal and abnormal state prompts. however, since clip focuses on building correspondence between paired text prompts and global image - level representations, the lack of fine - grained patch - level vision to text alignment limits its capability on precise visual anomaly localization. in this work, we propose anoclip for zero - shot anomaly localization. in the visual encoder, we introduce a training - free value - wise attention mechanism to extract intrinsic local tokens of clip for patch - level local description. from the perspective of text supervision, we particularly design a unified domain - aware contrastive state prompting template for fine - grained vision - language matching. on top of the proposed anoclip, we further introduce a test - time adaptation ( tta ) mechanism to refine visual anomaly localization results, where we optimize a lightweight adapter in the visual encoder using anoclip ' s pseudo - labels and noise - corrupted tokens. with both anoclip and tta, we significantly exploit the potential of clip for zero - shot anomaly localization and demonstrate the effectiveness of anoclip on various datasets. | arxiv:2308.15939 |
we determine the jet vertex for mueller - navelet jets and forward jets in the small - cone approximation for two particular choices of jet algoritms : the kt algorithm and the cone algorithm. these choices are motivated by the extensive use of such algorithms in the phenomenology of jets. the differences with the original calculations of the small - cone jet vertex by ivanov and papa, which is found to be equivalent to a formerly algorithm proposed by furman, are shown at both analytic and numerical level, and turn out to be sizeable. a detailed numerical study of the error introduced by the small - cone approximation is also presented, for various observables of phenomenological interest. for values of the jet " radius " r = 0. 5, the use of the small - cone approximation amounts to an error of about 5 % at the level of cross section, while it reduces to less than 2 % for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets. | arxiv:1501.07442 |
normally ordered forms of functions of boson operators are important in many contexts in particular concerning quantum field theory and quantum optics. beginning with the seminal work of katriel [ lett. nuovo cimento, 10 ( 13 ) : 565 - - 567, 1974 ], in the last few years, normally ordered forms have been shown to have a rich combinatorial structure, mainly in virtue of a link with the theory of partitions. in this paper, we attempt to enrich this link. by considering linear representations of noncrossing partitions, we define the notion of noncrossing normal ordering. given the growing interest in noncrossing partitions, because of their many unexpected connections ( like, for example, with free probability ), noncrossing normal ordering appears to be an intriguing notion. we explicitly give the noncrossing normally ordered form of the functions ( a ^ { r } ( a ^ { \ dag } ) ^ { s } ) ^ { n } ) and ( a ^ { r } + ( a ^ { \ dag } ) ^ { s } ) ^ { n }, plus various special cases. we are able to establish for the first time bijections between noncrossing contractions of these functions, k - ary trees and sets of lattice paths. | arxiv:quant-ph/0607074 |
we introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. the scheme allows to generate graph states such as 2d and 3d cluster states of growing size or ghz states over arbitrary distances, with a constant overhead per node / channel that is independent of the distance. the approach is genuine multipartite, and is based on the measurement - based implementation of multipartite hashing, an entanglement purification protocol that operates on a large ensemble together with local merging / connection of elementary building blocks. we analyze the performance of the scheme in a setting where local or global storage is limited, and compare it to bipartite and hybrid approaches that are based on the distribution of entangled pairs. we find that the multipartite approach offers a storage advantage, which results in higher efficiency and better performance in certain parameter regimes. we generalize our approach to arbitrary network topologies and different target graph states. | arxiv:1806.11562 |
in rotating magnetospheres planted on compact objects, there usually exist lightcylinders ( lc ), beyond which the rotation speed of the magnetic field lines exceeds the speed of light. the lc is a close analog to the horizon in gravity, and is a casual boundary for charged particles that are restricted to move along the magnetic field lines. in this work, it is proposed that there should be hawking - like radiation of charged particles from the lc of a rotating magnetosphere from the point of view of tunneling by using the field sheet metric. | arxiv:2111.05507 |
we propose a modified version of the horowitz - maldacena final - state boundary condition based upon a matter - radiation thermalization hypothesis on the black hole interior, which translates into a particular entangled state with thermal schmidt coefficients. we investigate the consequences of this proposal for matter entering the horizon, as described by a canonical density matrix characterized by the matter temperature $ t $. the emitted radiation is explicitly calculated and is shown to follow a thermal spectrum with an effective temperature $ t _ { eff } $. we analyse the evaporation process in the quasi - static approximation, highlighting important differences in the late stages with respect to the usual semiclassical evolution, and calculate the fidelity of the emitted hawking radiation relative to the infalling matter. | arxiv:hep-th/0611152 |
in a series of papers we have argued that the ' basic ' physical procedure of minimal coupling giving the quantum description of a hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation as a twisted weyl quantization \ cite { mp2 }. in this paper we shall present a review of some of these results with some modified proofs that allow a special focus on the dependence on the behavior of the magnetic field, having in view possible developments towards problems with unbounded magnetic fields. the main new result is contained in theorem 2. 9 and states that the the symbol of the evolution group of the self - adjoint operator defined by a real elliptic symbol of strictly positive order in a smooth bounded magnetic field is in the associated magnetic moyal algebra, i. e. leaves invariant the space of schwartz test functions and its dual | arxiv:1804.07636 |
the $ k \ bar { k } ^ * $ interaction lagrangian is constructed when the $ su ( 3 ) $ hidden gauge symmetry is taken into account, and then the $ k \ bar { k } ^ * $ potential is obtained. in the low energy region, the $ k \ bar { k } ^ * $ potential mainly comes from the contribution of the $ t - $ channel interaction by exchanging $ \ rho $, $ \ omega $ and $ \ varphi $ mesons, respectively. the $ k \ bar { k } ^ * $ amplitude is investigated by solving the bethe - salpeter equation in the unitary coupled - channel approximation, where the loop function of the vector and pseudoscalar mesons are evaluated in the dimensional regularization scheme, and the contribution of the longitudinal part of the intermediate vector meson propagator is included in the calculation. finally, it is found that a resonance state of $ k \ bar { k } ^ * $ is generated in the isospin $ i = 0 $ sector, which might correspond to the $ f _ 1 ( 1420 ) $ particle in the review of the particle data group ( pdg ). moreover, in the isospin $ i = 1 $ sector, a pole of the $ k \ bar { k } ^ * $ amplitude is detected at $ 1425 - i316 $ mev on the complex plane of the total energy in the center of mass system, which is higher than the $ k \ bar { k } ^ * $ threshold. thus this pole might be a resonance state of $ k \ bar { k } ^ * $ although no counterpart has been found in the pdg review. | arxiv:1808.08358 |
the present paper is concerned a class of quasi - linear elliptic degenerate equations. the degenerate operator comes from the analysis of manifolds with corner singularity. variational methods are applied to verify the existence of infinity many solutions for the problems. | arxiv:1908.07134 |
we construct an algebra of non - trivial homological operations on khovanov homology with coefficients in $ \ mathbb z _ 2 $ generated by two bockstein operations. we use the unified khovanov homology theory developed by the first author to lift this algebra to integral khovanov homology. we conjecture that these two algebras are infinite and present evidence in support of our conjectures. finally, we list examples of knots that have the same even and odd khovanov homology, but different actions of these homological operations. this confirms that the unified theory is a finer knot invariant than the even and odd khovanov homology combined. the case of reduced khovanov homology is also considered. | arxiv:1601.00798 |
we consider the plurality consensus problem among $ n $ agents. initially, each agent has one of $ k $ different opinions. agents choose random interaction partners and revise their state according to a fixed transition function, depending on their own state and the state of the interaction partners. the goal is to reach a consensus configuration in which all agents agree on the same opinion, and if there is initially a sufficiently large bias towards one opinion, that opinion should prevail. we analyze a synchronized variant of the undecided state dynamics defined as follows. the agents act in phases, consisting of a decision and a boosting part. in the decision part, any agent that encounters an agent with a different opinion becomes undecided. in the boosting part, undecided agents adopt the first opinion they encounter. we consider this dynamics in the population model and the gossip model. for the population model, our protocol reaches consensus ( w. h. p. ) in $ o ( \ log ^ 2 n ) $ parallel time, providing the first polylogarithmic result for $ k > 2 $ ( w. h. p. ) in this model. without any assumption on the bias, fast consensus has only been shown for $ k = 2 $ for the unsynchronized version of the undecided state dynamics [ clementi et al., mfcs ' 18 ]. we show that the synchronized variant of the undecided state dynamics reaches consensus ( w. h. p. ) in time $ o ( \ log ^ 2 n ) $, independently of the initial number, bias, or distribution of opinions. in both models, we guarantee that if there is an initial bias of $ \ omega ( \ sqrt { n \ log n } ) $, then ( w. h. p. ) that opinion wins. a simple extension of our protocol in the gossip model yields a dynamics that does not depend on $ n $ or $ k $, is anonymous, and has ( w. h. p. ) runtime $ o ( \ log ^ 2 n ) $. this solves an open problem formulated by becchetti et al. ~ [ distributed computing, ~ 2017 ]. | arxiv:2103.10366 |
in this paper, we apply the combinatorial results on counting permutations with fixed pinnacle and vale sets to evaluate the special values of the spectral zeta functions of sturm - liouville differential operators. as applications, we get a combinatorial formula for the special values of spectral zeta functions and give a new explicit formula for bernoulli numbers. | arxiv:2303.10004 |
hubble space telescope images of the young galactic supernova remnant cassiopeia a reveal a far larger population of outlying, high - velocity knots of ejecta with a broader range of chemical properties than previously suspected. we identify three main classes of outer ejecta : 1 ) knots dominated by [ n ii ] 6548, 6583 emission ; 2 ) knots dominated by oxygen emission lines especially [ o ii ] 7319, 7330 ; and 3 ) knots with emission line strengths similar to the [ s ii ] strong fmk ejecta commonly seen in the main emission shell. the discovery of a significant population of o - rich ejecta situated in between the suspected n - rich outer photospheric layer and s - rich fmk - like ejecta suggests that the cas a progenitor ' s chemical layers were not completely disrupted by the supernova explosion outside of the remnant ' s ne and sw high velocity ` jet ' regions. in addition, we find the majority of o - rich outer ejecta at projected locations out beyond ( v = 6500 - 9000 km / s ) the remnant ' s fastest moving fe - rich x - ray emission material ( 6000 km / s ) seen in chandra and xmm data along the eastern limb. this suggests that penetration of fe - rich material up through the s and si - rich mantle did not extend past the progenitor ' s n or o - rich outer layers for at least this section of the remnant. | arxiv:astro-ph/0509067 |
the identification of the exact path that packets are routed in the network is quite a challenge. this paper presents a novel, efficient traceback strategy in combination with a defence system against distributed denial of service ( ddos ) attacks named tracemax. a single packets can be directly traced over many more hops than the current existing techniques allow. it let good connections pass while bad ones get thwarted. initiated by the victim the routers in the network cooperate in tracing and become automatically self - organised and self - managed. the novel concept support analyses of packet flows and transmission paths in a network infrastructure. it can effectively reduce the effect of common bandwidth and resource consumption attacks and foster in addition early warning and prevention. | arxiv:2407.10985 |
building on an analogy with ordinary scalar field theories, an epsilon expansion for rank - 3 tensorial group field theories with gauge invariance condition is introduced. this allows to continuously interpolate between the dimension four group su ( 2 ) x u ( 1 ) and the dimension three su ( 2 ). in the first situation, there is a unique marginal 4 - valent coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. in the su ( 2 ) case, the presence of two marginally relevant 6 - valent coupling constants and one 4 - valent super - renormalizable interaction spoils this interesting property. however, the existence of a non - trivial fixed point is established in dimension four minus epsilon, hence suggesting that the su ( 2 ) theory might be asymptotically safe. to pave the way to future non - perturbative calculations, the present perturbative results are discussed in the framework of the effective average action. | arxiv:1411.5385 |
wave propagation is a common occurrence in all of physics. a linear approximation provides a simpler way to describe various fields related to observable phenomena in laboratory physics as well as astronomy and cosmology, allowing us to probe gravitation through its effect on the trajectories of particles associated with those fields. this paper proposes a unified framework to describe the wave propagation of a set of interacting tensor fields that obey coupled homogeneous linear second - order partial differential equations for arbitrary curved spacetimes, both lorentzian and metric - affine. we use jwkb ans \ " atze for all fields, written in terms of a perturbation parameter proportional to a representative wavelength among them, deriving a set of hierarchical algebraic and differential equations that link the fields ' phases and different order amplitudes. this allows us to reobtain the well - known laws of geometrical optics and beyond geometrical optics in a generalized form, showing that these laws are independent of the rank of the fields involved. this is true as long as what we refer to as the kinetic tensor of a given field satisfies a set of diagonality conditions, which further imply a handful of simplifications on the transport equations obtained in the subleading orders of the jwkb ans \ " atze. we explore these results in several notable examples in lorentzian and metric - affine spacetimes, illustrating the reach of our derivations in general relativity, reduced horndeski theories, spacetimes with completely antisymmetric torsion and weyl spacetimes. the formalism presented herein lays the groundwork for the study of rays associated with different types of waves in curved spacetimes and provides the tools to compute modifications to their brightness evolution laws, consequential distance duality relations, and beyond geometrical optics phenomena. | arxiv:2407.04627 |
we present monte carlo radiative transfer simulations for spiral galaxies modelled as a stellar disk and a two - phase clumpy dust distribution. we divide the volume occupied by the dust into a three - dimensional grid and assign each cell a clump or smooth medium status. cell dimension, clump dust mass and spatial distribution are derived from the observed properties of giant molecular clouds and molecular gas in the galaxy. we produce models for several values of the optical depth and fraction of the interstellar medium residing in clumps. as a general result, clumpy models are less opaque than the corresponding homogeneous models. for the adopted parameters, the increase in the fraction of energy that escapes the disk is moderate, resulting in surface brightness profiles that are less than one magnitude brighter than those of the homogeneous models. the effects of clumping are larger for edge - on views of the disk. this is in contrast with previous preliminary results for clumping in the literature. we show how differences arise from the different parametrisation and clump distribution adopted. we also consider models in which a fraction of the stellar radiation is emitted within the clumps. in this case, galaxies are less transparent than in the case when only dust is clumped. the opacity can be even higher than in the homogeneous case, depending on the fraction of embedded stellar emission. we point out the implications of the results for the determination of the opacity and dust mass of spiral galaxies. | arxiv:astro-ph/9909395 |
cuprates, ferropnictides and ferrochalcogenides are three classes of unconventional high - temperature superconductors, who share similar phase diagrams in which superconductivity develops after a magnetic order is suppressed, suggesting a strong interplay between superconductivity and magnetism, although the exact picture of this interplay remains elusive. here we show that there is a direct bridge connecting antiferromagnetic exchange interactions determined in the parent compounds of these materials to the superconducting gap functions observed in the corresponding superconducting materials. high superconducting transition temperature is achieved when the fermi surface topology matches the form factor of the pairing symmetry favored by local magnetic exchange interactions. our result offers a principle guide to search for new high temperature superconductors. | arxiv:1107.1334 |
for the approximation of solutions for stochastic partial differential equations, numerical methods that obtain a high order of convergence and at the same time involve reasonable computational cost are of particular interest. we therefore propose a new numerical method of exponential stochastic runge - kutta type that allows for convergence with a temporal order of up to 3 / 2 and that can be combined with several spatial discretizations. the developed family of derivative - free schemes is tailored to stochastic partial differential equations of nemytskii - type, i. e., with pointwise multiplicative noise operators. we prove the strong convergence of these schemes in the root mean - square sense and present some numerical examples that reveal the theoretical results. | arxiv:2412.08299 |
we describe the encoding of multiple qubits per atom in trapped atom quantum processors and methods for performing both intra - and inter - atomic gates on participant qubits without disturbing the spectator qubits stored in the same atoms. we also introduce techniques for selective state preparation and measurement of individual qubits that leave the information encoded in the other qubits intact, a capability required for qubit quantum error correction. the additional internal states needed for polyqubit processing are already present in atomic processors, suggesting that the resource cost associated with this multiplicative increase in qubit number could be a good bargain in the short to medium term. | arxiv:2210.15484 |
the rosat pspc pulse height spectrum of the peculiar he - rich hot white dwarf kpd 0005 + 5106 provided a great surprise when first analysed by fleming, werner & barstow ( 1993 ). it defied the best non - lte modelling attempts in terms of photospheric emission from he - dominated atmospheres including c, n and o and was instead interpreted as the first evidence for a coronal plasma around a white dwarf. we show here that a recent high resolution chandra letgs spectrum has more structure than expected from a thermal bremsstrahlung continuum and lacks the narrow lines of h - like and he - like c expected from a coronal plasma. moreover, a coronal model requires a total luminosity more than two orders of magnitude larger than that of the star itself. instead, the observed 20 - 80 aa flux is consistent with photospheric models containing trace amounts of heavier elements such as fe. the soft x - ray flux is highly sensitive to the adopted metal abundance and provides a metal abundance diagnostic. the weak x - ray emission at 1 kev announced by o ' dwyer et al ( 2003 ) instead cannot arise from the photosphere and requires alternative explanations. we echo earlier speculation that such emission arises in a shocked wind. despite the presence of uv - optical o viii lines from transitions between levels n = 7 - 10, no x - ray o viii ly alpha flux is detected. we show that o viii lyman photons can be trapped by resonant scattering within the emitting plasma and destroyed by photoelectric absorption. | arxiv:astro-ph/0502051 |
turbo codes and crc codes are usually decoded separately according to the serially concatenated inner codes and outer codes respectively. in this letter, we propose a hybrid decoding algorithm of turbo - crc codes, where the outer codes, crc codes, are not used for error detection but as an assistance to improve the error correction performance. two independent iterative decoding and reliability based decoding are carried out in a hybrid schedule, which can efficiently decode the two different codes as an entire codeword. by introducing an efficient error detecting method based on normalized euclidean distance without crc check, significant gain can be obtained by using the hybrid decoding method without loss of the error detection ability. | arxiv:2003.11233 |
we present analysis of the near - infrared spectra of 114 rest - frame uv - selected star - forming galaxies at z ~ 2. by combining the h - alpha spectra with photometric measurements from observed 0. 3 - - 8 micron, we assess the relationships between kinematics, dynamical masses, inferred gas fractions, and stellar masses and ages. the h - alpha line widths give a mean dynamical mass m _ dyn = 6. 9 + / - 0. 6 x 10 ^ 10 msun within a typical radius of ~ 6 kpc, after excluding agn. the average dynamical mass is ~ 2 times larger than the average stellar mass, and the two agree to within a factor of several for most objects. however, ~ 15 % of the sample has m _ dyn > > m _ star. these objects are best fit by young stellar populations and tend to have high h - alpha equivalent widths, suggesting that they are young starbursts with large gas masses. rest - frame optical luminosity and velocity dispersion are correlated with 4 sigma significance. using the local empirical correlation between star formation rate per unit area and gas surface density, we estimate the mass of the gas associated with star formation, and find a mean gas fraction of ~ 50 % and a strong decrease in gas fraction with increasing stellar mass. the masses of gas and stars combined are considerably better correlated with the dynamical masses than are the stellar masses alone, and agree to within a factor of three for 85 % of the sample. the combination of kinematic measurements, estimates of gas masses, and stellar population properties suggest that the factor of ~ 500 range in stellar mass across the sample cannot be fully explained by intrinsic differences in the total masses of the galaxies, which vary by a factor of ~ 40 ; the remaining variation is due to the evolution of the stellar population and the conversion of gas into stars. [ abridged ] | arxiv:astro-ph/0604041 |
we develop an analytic formalism and derive new exact relations that express the short - time dispersion of fluid particles via the single - time velocity correlation functions in homogeneous isotropic and incompressible turbulence. the formalism establishes a bridge between single - time eulerian and long - time lagrangian pictures of turbulent flows. in particular, we derive an exact formula for a short - term analog of the long - time richardson law, and we identify a conservation law of turbulent dispersion which is true even in non - stationary turbulence. | arxiv:1302.6693 |
discharge capillary - based active plasma lenses are a promising new technology for strongly focusing charged particle beams, especially when combined with novel high gradient acceleration methods. still, many questions remain concerning such lenses, including their transverse field uniformity, limitations due to plasma wakefields and whether they can be combined in multi - lens lattices in a way to cancel chromaticity. these questions will be addressed in a new plasma lens experiment at the clear user facility at cern. all the subsystems have been constructed, tested and integrated into the clear beam line, and are ready for experiments starting late 2017. | arxiv:1801.00956 |
monolayer transition metal dichalcogenides ( 2d ) and zero dimensional quantum dots ( qd ) are known to have unique optical properties in their individual limit such as high binding energy of excitons. the combination of these two systems is of particular interest in understanding various aspects of energy transfer, charge transfer, dynamics of excitons, etc. in this manuscript, we report the anomalous photoluminescence ( pl ) emission in one such heterostructure mos2 - cdse qd. we observe multiple exciton emission peaks of the heterostructure on hbn substrate which are absent on sio2. our observation open up the questions, whether the local potential due to the lattice mismatch between mos2 and hbn has any role in deciding the emission of these peaks or the strain eld of mos2 and hbn is the reason for the emergence of multiple emission. in addition, the altered quantum potential of qd due the presence of hbn and mos2 may also leads to such multiple emissions. | arxiv:2107.12271 |
we numerically demonstrate that domain walls can be used as spin wave waveguides. we show that gapless spin waves bounded inside a domain wall can be guided by the domain wall. for bloch walls, we further show that the bound spin waves can pass through bloch lines and corners without reflection. this finding makes domain - wall - based spin wave devices possible. | arxiv:1512.05965 |
this master ' s thesis discusses an important issue regarding how algorithmic decision making ( adm ) is used in crime forecasting. in america forecasting tools are widely used by judiciary systems for making decisions about risk offenders based on criminal justice for risk offenders. by making use of such tools, the judiciary relies on adm in order to make error free judgement on offenders. for this purpose, one of the quality measures for machine learning techniques which is widly used, the $ auc $ ( area under curve ), is compared to and contrasted for results with the $ ppv _ k $ ( positive predictive value ). keeping in view the criticality of judgement along with a high dependency on tools offering adm, it is necessary to evaluate risk tools that aid in decision making based on algorithms. in this methodology, such an evaluation is conducted by implementing a common machine learning approach called binary classifier, as it determines the binary outcome of the underlying juristic question. this thesis showed that the $ ppv _ k $ ( positive predictive value ) technique models the decision of judges much better than the $ auc $. therefore, this research has investigated whether there exists a classifier for which the $ ppv _ k $ deviates from $ auc $ by a large proportion. it could be shown that the deviation can rise up to 0. 75. in order to test this deviation on an already in used classifier, data from the fourth generation risk assement tool compas was used. the result were were quite alarming as the two measures derivate from each other by 0. 48. in this study, the risk assessment evaluation of the forecasting tools was successfully conducted, carefully reviewed and examined. additionally, it is also discussed whether such systems used for the purpose of making decisions should be socially accepted or not. | arxiv:1804.01557 |
we consider a stochastic optimal exit time feedback control problem. the bellman equation is solved approximatively via the policy iteration algorithm on a polynomial ansatz space by a sequence of linear equations. as high degree multi - polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. we employ tensor - train methods to account for this problem. the approximation process within the policy iteration is done via a least - squares ansatz and the integration is done via monte - carlo methods. numerical evidences are given for the ( multi dimensional ) double well potential and a three - hole potential. | arxiv:2010.04465 |
this chapter introduces openstreetmap - a crowd - sourced, worldwide mapping project and geospatial data repository - to illustrate its usefulness in quickly and easily analyzing and visualizing planning and design outcomes in the built environment. it demonstrates the osmnx toolkit for automatically downloading, modeling, analyzing, and visualizing spatial big data from openstreetmap. we explore patterns and configurations in street networks and buildings around the world computationally through visualization methods - including figure - ground diagrams and polar histograms - that help compress urban complexity into comprehensible artifacts that reflect the human experience of the built environment. ubiquitous urban data and computation can open up new urban form analyses from both quantitative and qualitative perspectives. | arxiv:2008.12142 |
the maximum strength of gravity at the surface of an object of a given mass is not attained for a spherical shape, but for a small departure from sphericity. | arxiv:physics/0312029 |
the distinction between point and line resolution in transmission electron microscopy ( tem ) arises because an ability to image sub - 0. 2 nm fringes is a necessary, but not a sufficient, condition for imaging individual atoms. in scanned tip microscopy, as in tem, empirical data on instrument response should precede assertions about point resolution. in the ` ` slow scan limit ' ', time - domain noise and geometry effects decouple, and tip shape can take on the role of a 2 - dimensional impulse response function. we indicate here that nuclear track pits can be used to quantitatively measure tip geometry with nanometer - scale resolution in three dimensions, that stationary tip images provide a robust measure of time - domain instabilities, and that when these data are taken before and after imaging an unknown, images with instrument response quantitatively constrained by experiment are possible. specimen - induced tip effects also become measurable in situ. | arxiv:physics/9712003 |
the purpose of this study is to provide a reproducible framework in the use of the green - kubo formalism to extract transport coefficients. more specifically, in the case of shear viscosity, we investigate the limitations and technical details of fitting the auto - correlation function to a decaying exponential. this fitting procedure is found to be applicable for systems interacting both through constant and energy - dependent cross - sections, although this is only true for sufficiently dilute systems in the latter case. we find that the optimal fit technique consists in simultaneously fixing the intercept of the correlation function and use a fitting interval constrained by the relative error on the correlation function. the formalism is then applied to the full hadron gas, for which we obtain the shear viscosity to entropy ratio. | arxiv:1709.00369 |
tunneling spectroscopy of epitaxial ( 100 ) oriented \ chem { yba _ 2cu _ 3o _ { 7 - \ delta } } films was performed using an stm at 4. 2 k. on atomically smooth areas, tunneling spectra revealing clear u - shaped gaps with relatively low zero bias conductance were measured. these spectra can be well fitted to the tunneling theory into a d - wave superconductor only when introducing a strong dependence of the tunneling probability on the wave - vector \ emph { \ textbf { k } }. possible origins for this \ emph { \ textbf { k } } - selectivity in stm measurements will be discussed. on other areas, v - shaped gaps as well as zero bias conductance peaks are observed, indicating relaxation of \ emph { \ textbf { k } } - selectivity and the effect of nanofaceting, respectively. | arxiv:cond-mat/0305257 |
one main task of smooth dynamical systems consists in finding a good decomposition into elementary pieces of the dynamics. this paper contributes to the study of chain - recurrence classes. it is known that $ c ^ 1 $ - generically, each chain - recurrence class containing a periodic orbit is equal to the homoclinic class of this orbit. our result implies that in general this property is fragile. we build a c1 - open set u of tame diffeomorphisms ( their dynamics only splits into finitely many chain - recurrence classes ) such that for any diffeomorphism in a c - infinity - dense subset of u, one of the chain - recurrence classes is not transitive ( and has an isolated point ). moreover, these dynamics are obtained among partially hyperbolic systems with one - dimensional center. r \ ' esum \ ' e : dynamique mod \ ' er \ ' ee et transitivit \ ' e robuste. l ' un des buts des syst \ ` emes dynamiques consiste \ ` a trouver une bonne d \ ' ecomposition de la dynamique en pi \ ` eces \ ' el \ ' ementaires. cet article contribue \ ` a l ' \ ' etude des classes de r \ ' ecurrence par cha \ ^ ines. on sait que c1 - g \ ' en \ ' eriquement, chaque classe de r \ ' ecurrence par cha \ ^ ines contenant une orbite p \ ' eriodique coincide avec la classe homocline de cette orbite. notre r \ ' esultat montre que cette propri \ ' et \ ' e est en g \ ' en \ ' erale fragile. nous construisons un ouvert u de diff \ ' eomorphismes mod \ ' er \ ' es ( leur dynamique ne se d \ ' ecompose qu ' en un nombre fini de classes de r \ ' ecurrence par cha \ ^ ines ) tel que pour tout diff \ ' eomorphisme appartenant \ ` a un sous - ensemble c - infini - dense de u, une des classes de r \ ' ecurrence par cha \ ^ ines n ' est pas transitive ( elle a un point | arxiv:1112.1002 |
we prove that if $ m $ is a cw - complex, then the homotopy type of the skeletal filtration of $ m $ does not depend on the cell decomposition of $ m $ up to wedge products with $ n $ - disks $ d ^ n $, when the later are given their natural cw - decomposition with unique cells of order 0, $ ( n - 1 ) $ and $ n $ ; a result resembling j. h. c. whitehead ' s work on simple homotopy types. from the colimit theorem for the fundamental crossed complex of a cw - complex ( due to r. brown and p. j. higgins ), follows an algebraic analogue for the fundamental crossed complex $ \ pi ( m ) $ of the skeletal filtration of $ m $, which thus depends only on the homotopy type of $ m $ ( as a space ) up to free product with crossed complexes of the type $ \ pi ( d ^ n ), n \ in n $. this expands an old result ( due to j. h. c. whitehead ) asserting that the homotopy type of $ \ pi ( m ) $ depends only on the homotopy type of $ m $. we use these results to define a homotopy invariant $ i _ a $ of cw - complexes for any finite crossed complex $ a $. we interpret it in terms of the weak homotopy type of the function space $ top ( ( m, * ), ( | a |, * ) ) $, where $ | a | $ is the classifying space of the crossed complex $ a $. | arxiv:math/0605364 |
multipliers have been recently introduced as operators for bessel sequences and frames in hilbert spaces. these operators are defined by a fixed multiplication pattern ( the symbol ) which is inserted between the analysis and synthesis operators. in this paper, we will generalize the concept of bessel multipliers for p - bessel and p - riesz sequences in banach spaces. it will be shown that bounded symbols lead to bounded operators. symbols converging to zero induce compact operators. furthermore, we will give sufficient conditions for multipliers to be nuclear operators. finally, we will show the continuous dependency of the multipliers on their parameters. | arxiv:1004.5212 |
we establish the consistency of an algorithm of mondrian forests, a randomized classification algorithm that can be implemented online. first, we amend the original mondrian forest algorithm, that considers a fixed lifetime parameter. indeed, the fact that this parameter is fixed hinders the statistical consistency of the original procedure. our modified mondrian forest algorithm grows trees with increasing lifetime parameters $ \ lambda _ n $, and uses an alternative updating rule, allowing to work also in an online fashion. second, we provide a theoretical analysis establishing simple conditions for consistency. our theoretical analysis also exhibits a surprising fact : our algorithm achieves the minimax rate ( optimal rate ) for the estimation of a lipschitz regression function, which is a strong extension of previous results to an arbitrary dimension. | arxiv:1711.02887 |
we demonstrate two techniques for studying the features of three - level systems driven by two lasers ( called control and probe ), when the transitions are doppler broadened as in room - temperature vapor. for $ \ lambda $ - type systems, the probe laser is split to produce a counter - propagating pump beam that saturates the transition for the zero - velocity atoms. probe transmission then shows doppler - free peaks, which can even have sub - natural linewidth. for v - type systems, the transmission of the control beam is detected as the probe laser is scanned. the signal shows doppler - free peaks when the probe laser is resonant with transitions for the zero - velocity group. both techniques greatly simplify the study of three - level systems since theoretical predictions can be directly compared without complications from doppler broadening and the presence of multiple hyperfine levels in the spectrum. | arxiv:physics/0510088 |
we review various theoretical approaches for the equation of state ( eos ) of dense matter, relevant for the description of core - collapse supernovae, compact stars and compact star mergers. the emphasis is put on models that are applicable to all of these scenarios. such eos models have to cover large ranges in baryon number density, temperature and isospin asymmetry. the characteristics of matter change dramatically within these ranges, from a mixture of nucleons, nuclei, and electrons to uniform, strongly interacting matter containing nucleons, and possibly other particles such as hyperons or quarks. as the development of an eos requires joint efforts from many directions we consider different theoretical approaches and discuss relevant experimental and observational constraints which provide insights for future research. finally, results from applications of the discussed eos models are summarized. | arxiv:1610.03361 |
in this article we study the one - dimensional dynamics of elastic collisions of particles with positive and negative mass. we show that such systems are equivalent to billiards induced by an inner product of possibly indefinite signature, we characterize the systems with finitely many collisions and we prove that a small particle of negative mass between two particles of positive mass acts like an attracting particle with discrete acceleration ( at the collisions ) provided that the total kinetic energy is negative. in the limit of the negative mass going to zero, with fixed negative kinetic energy, we obtain a continuous acceleration with potential energy of the form $ u ( r ) = - k / r ^ 2 $. | arxiv:1808.10547 |
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