7,747 research outputs found
The Ones Who Walk Away From the Ocean
When a mermaid mysteriously appears on the shore of a Northern island, the town\u27s children become enthralled with the newfound mythic creature, while the adults become wary and untrusting
Entanglements in Quiescent and Sheared Polymer Melts
We visualize entanglements in polymer melts using molecular dynamics
simulation. A bead at an entanglement interacts persistently for long times
with the non-bonded beads (those excluding the adjacent ones in the same
chain). The interaction energy of each bead with the non-bonded beads is
averaged over a time interval much longer than microscopic times but
shorter than the onset time of tube constraints . Entanglements
can then be detected as hot spots consisting of several beads with relatively
large values of the time-averaged interaction energy. We next apply a shear
flow with rate much faster than the entangle motion. With increasing strain the
chains take zigzag shapes and a half of the hot spots become bent. The chains
are first stretched as a network but, as the bends approach the chain ends,
disentanglements subsequently occur, leading to stress overshoot observed
experimentally.Comment: 19 pages, 11 figure
Veering triangulations admit strict angle structures
Agol recently introduced the concept of a veering taut triangulation, which
is a taut triangulation with some extra combinatorial structure. We define the
weaker notion of a "veering triangulation" and use it to show that all veering
triangulations admit strict angle structures. We also answer a question of
Agol, giving an example of a veering taut triangulation that is not layered.Comment: 15 pages, 9 figure
Tighter Relations Between Sensitivity and Other Complexity Measures
Sensitivity conjecture is a longstanding and fundamental open problem in the
area of complexity measures of Boolean functions and decision tree complexity.
The conjecture postulates that the maximum sensitivity of a Boolean function is
polynomially related to other major complexity measures. Despite much attention
to the problem and major advances in analysis of Boolean functions in the past
decade, the problem remains wide open with no positive result toward the
conjecture since the work of Kenyon and Kutin from 2004.
In this work, we present new upper bounds for various complexity measures in
terms of sensitivity improving the bounds provided by Kenyon and Kutin.
Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1}
s(f); these in turn imply various corollaries regarding the relation between
sensitivity and other complexity measures, such as block sensitivity, via known
results. The gap between sensitivity and other complexity measures remains
exponential but these results are the first improvement for this difficult
problem that has been achieved in a decade.Comment: This is the merged form of arXiv submission 1306.4466 with another
work. Appeared in ICALP 2014, 14 page
Autocorrelation of Random Matrix Polynomials
We calculate the autocorrelation functions (or shifted moments) of the
characteristic polynomials of matrices drawn uniformly with respect to Haar
measure from the groups U(N), O(2N) and USp(2N). In each case the result can be
expressed in three equivalent forms: as a determinant sum (and hence in terms
of symmetric polynomials), as a combinatorial sum, and as a multiple contour
integral. These formulae are analogous to those previously obtained for the
Gaussian ensembles of Random Matrix Theory, but in this case are identities for
any size of matrix, rather than large-matrix asymptotic approximations. They
also mirror exactly autocorrelation formulae conjectured to hold for
L-functions in a companion paper. This then provides further evidence in
support of the connection between Random Matrix Theory and the theory of
L-functions
The transform likelihood ratio method for rare event simulation with heavy tails
We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method
Learning Incoherent Subspaces: Classification via Incoherent Dictionary Learning
In this article we present the supervised iterative projections and rotations (s-ipr) algorithm, a method for learning discriminative incoherent subspaces from data. We derive s-ipr as a supervised extension of our previously proposed iterative projections and rotations (ipr) algorithm for incoherent dictionary learning, and we employ it to learn incoherent sub-spaces that model signals belonging to different classes. We test our method as a feature transform for supervised classification, first by visualising transformed features from a synthetic dataset and from the ‘iris’ dataset, then by using the resulting features in a classification experiment
Random Time Forward Starting Options
We introduce a natural generalization of the forward-starting options, first
discussed by M. Rubinstein. The main feature of the contract presented here is
that the strike-determination time is not fixed ex-ante, but allowed to be
random, usually related to the occurrence of some event, either of financial
nature or not. We will call these options {\bf Random Time Forward Starting
(RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis,
we can exhibit arbitrage free prices, which can be explicitly computed in many
classical market models, at least under independence between the random time
and the assets' prices. Practical implementations of the pricing methodologies
are also provided. Finally a credit value adjustment formula for these OTC
options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur
Exploiting Machine Learning to Subvert Your Spam Filter
Using statistical machine learning for making security decisions introduces new vulnerabilities in large scale systems. This paper shows how an adversary can exploit statistical machine learning, as used in the SpamBayes spam filter, to render it useless—even if the adversary’s access is limited to only 1 % of the training messages. We further demonstrate a new class of focused attacks that successfully prevent victims from receiving specific email messages. Finally, we introduce two new types of defenses against these attacks.
Dynamic multilateral markets
We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish
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