282,700 research outputs found
Gap Edit Distance via Non-Adaptive Queries: Simple and Optimal
We study the problem of approximating edit distance in sublinear time. This
is formalized as a promise problem -Gap Edit Distance, where the input
is a pair of strings and parameters , and the goal is to return
YES if and NO if . Recent years have witnessed
significant interest in designing sublinear-time algorithms for Gap Edit
Distance.
We resolve the non-adaptive query complexity of Gap Edit Distance, improving
over several previous results. Specifically, we design a non-adaptive algorithm
with query complexity , and further prove that
this bound is optimal up to polylogarithmic factors.
Our algorithm also achieves optimal time complexity
whenever . For , the
running time of our algorithm is . For the
restricted case of , this matches a known result [Batu, Erg\"un,
Kilian, Magen, Raskhodnikova, Rubinfeld, and Sami, STOC 2003], and in all other
(nontrivial) cases, our running time is strictly better than all previous
algorithms, including the adaptive ones
Changing Channels of Technology: Disaster and (Im)mortality in Don DeLilloâs White Noise, Cosmopolis and Zero K
This article examines the changing representation of technology in three
of DeLilloâs novels, White Noise, Cosmopolis and Zero K, and traces the conceptual
and philosophical developments in his writing concerning the two
key themes of disaster and mortality. Disasters witnessed through technological
means consistently distance the ârealâ from the event in earlier
work such as White Noise, whereas in Cosmopolis, Eric Packer, the central
character, yearns for disasters to happen to himself. DeLilloâs latest novel
Zero K represents a clear sense of ending and longing for disaster. Secondly,
technology changes from promoting a fear of death in earlier works,
to a fear of life in Zero K, highlighting the bleakness of life in a world ruled\ud
by technology. This article will discuss these two progressions in detail
across the three novels, followed by a conclusion of the comparisons titled
âChanging Channelsâ for each theme, producing an original perspective of
the diachronic changes through DeLilloâs work
La k-PDTM : un coreset pour l'inférence géométrique
Analyzing the sub-level sets of the distance to a compact sub-manifold of R d is a common method in TDA to understand its topology. The distance to measure (DTM) was introduced by Chazal, Cohen-Steiner and MĂ©rigot in [7] to face the non-robustness of the distance to a compact set to noise and outliers. This function makes possible the inference of the topology of a compact subset of R d from a noisy cloud of n points lying nearby in the Wasserstein sense. In practice, these sub-level sets may be computed using approximations of the DTM such as the q-witnessed distance [10] or other power distance [6]. These approaches lead eventually to compute the homology of unions of n growing balls, that might become intractable whenever n is large. To simultaneously face the two problems of large number of points and noise, we introduce the k-power distance to measure (k-PDTM). This new approximation of the distance to measure may be thought of as a k-coreset based approximation of the DTM. Its sublevel sets consist in union of k-balls, k << n, and this distance is also proved robust to noise. We assess the quality of this approximation for k possibly dramatically smaller than n, for instance k = n 1 3 is proved to be optimal for 2-dimensional shapes. We also provide an algorithm to compute this k-PDTM.L'analyse des sous niveaux de la fonction distance Ă une variĂ©tĂ© compacte de R d est trĂšs frĂ©quente en analyse topologique des donnĂ©es, avec pour objectif d'en comprendre la topologie. La distance Ă la mesure (DTM) a Ă©tĂ© introduite par Chazal, Cohen-Steiner et MĂ©rigot avec l'objectif de remĂ©dier au caractĂšre non robuste au bruit et aux donnĂ©es aberrantes de la distance Ă un compact. Cette fonction rend possible l'infĂ©rence de la topologie d'un sous-ensemble compact de R d Ă partir d'un nuage de n points tirĂ©s dans un voisinage proche de la sous-variĂ©tĂ© au sens de Wasserstein. En pratique, les sous-ensembles de niveau de cette fonction peuvent ĂȘtre estimĂ©s en utilisant des approximations de la DTM tels que la q-witnessed distance ou d'autres fonctions puissance. Ces approches reviennent Ă calculer l'homologie de l'union de n boules, ce qui devient impossible en pratique lorsque n devient trop grand. Afin de traiter le problĂšme du grand nombre de points et du bruit, on introduit la fonction k-puissance distance Ă la mesure (k-PDTM). Cette nouvelle approximation de la distance Ă la mesure peut ĂȘtre vue une approximation de la DTM s'appuyant sur un -coreset. Ses sous-niveaux seront alors des unions de k boules pour k<<n, et cette fonction est Ă©galement robuste au bruit. On Ă©tudie la qualitĂ© de cette approximation lorsque k est trĂšs petit par rapport Ă n. Par exemple, le choix de k=n^{1/3} est optimal pour des formes en dimension 2. On fournit Ă©galement un algorithme pour calculer cette fonction k-PDTM
Robust Geometry Estimation using the Generalized Voronoi Covariance Measure
The Voronoi Covariance Measure of a compact set K of R^d is a tensor-valued
measure that encodes geometric information on K and which is known to be
resilient to Hausdorff noise but sensitive to outliers. In this article, we
generalize this notion to any distance-like function delta and define the
delta-VCM. We show that the delta-VCM is resilient to Hausdorff noise and to
outliers, thus providing a tool to estimate robustly normals from a point cloud
approximation. We present experiments showing the robustness of our approach
for normal and curvature estimation and sharp feature detection
Against the Nihilism of Suffering and Death: Richard E. K. Kim and His Works
This article examines the life and works of Richard E. K. Kim (1932â2009), a first-generation Korean diasporic writer in the United States. It focuses on how Kim struggled to overcome the nihilism of suffering and death that derived from colonialism and the Korean War through his literary works. Kim witnessed firsthand these two major historical events, which caused irrevocable psychological and physical damage to many people of his generation. In his autobiographical fiction, he conveys painful memories of the events by reviving the voices of people in that era. What his works offer us goes beyond vivid memories of the past, however; they also present the power of forgiveness as a condition to overcome the nihilism of suffering and death. Remembrance and forgiveness are, therefore, two major thematic pillars of his works that enable us to connect to these difficult and traumatic times. These themes are portrayed in such a gripping way mainly because Kim tried to maintain a certain distanceâan emotional and linguistic distanceâfrom the familiar, in order to elucidate the reality of the human condition: an ontological position of the exile from which he produced his works. This article argues that Kimâs works provide us the possibility to transcend the nihilism of historical trauma through articulating the meaning of remembrance and forgiveness from his self-assumed position of exile. Keywords: Richard E. K. Kim, diasporic writer, Lost Names, The Martyred, Searching for Lost Times, Japanese colonialism, Korean War, remembrance, forgivenes
Deterministic Digital Clustering of Wireless Ad Hoc Networks
We consider deterministic distributed communication in wireless ad hoc
networks of identical weak devices under the SINR model without predefined
infrastructure. Most algorithmic results in this model rely on various
additional features or capabilities, e.g., randomization, access to geographic
coordinates, power control, carrier sensing with various precision of
measurements, and/or interference cancellation. We study a pure scenario, when
no such properties are available. As a general tool, we develop a deterministic
distributed clustering algorithm. Our solution relies on a new type of
combinatorial structures (selectors), which might be of independent interest.
Using the clustering, we develop a deterministic distributed local broadcast
algorithm accomplishing this task in rounds, where
is the density of the network. To the best of our knowledge, this is
the first solution in pure scenario which is only polylog away from the
universal lower bound , valid also for scenarios with
randomization and other features. Therefore, none of these features
substantially helps in performing the local broadcast task. Using clustering,
we also build a deterministic global broadcast algorithm that terminates within
rounds, where is the diameter of the
network. This result is complemented by a lower bound , where is the path-loss parameter of the
environment. This lower bound shows that randomization or knowledge of own
location substantially help (by a factor polynomial in ) in the global
broadcast. Therefore, unlike in the case of local broadcast, some additional
model features may help in global broadcast
Experimental Demonstration of Macroscopic Quantum Coherence in Gaussian States
We witness experimentally the presence of macroscopic coherence in Gaussian
quantum states using a recently proposed criterion (E.G. Cavalcanti and M.
Reid, Phys. Rev. Lett. 97, 170405 (2006)). The macroscopic coherence stems from
interference between macroscopically distinct states in phase space and we
prove experimentally that even the vacuum state contains these features with a
distance in phase space of shot noise units (SNU). For squeezed
states we found macroscopic superpositions with a distance of up to
SNU. The proof of macroscopic quantum coherence was investigated
with respect to squeezing and purity of the states.Comment: 5 pages, 6 figure
Witnessed entanglement and the geometric measure of quantum discord
We establish relations between geometric quantum discord and entanglement
quantifiers obtained by means of optimal witness operators. In particular, we
prove a relation between negativity and geometric discord in the
Hilbert-Schmidt norm, which is slightly different from a previous conjectured
one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the
geometric discord with the trace norm, better bounds can be obtained. We
illustrate our results numerically.Comment: 8 pages + 3 figures. Revised version with erratum for PRA 86, 024302
(2012). Simplified proof that discord is bounded by entanglement in any nor
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