121 research outputs found
Scheduling with Outliers
In classical scheduling problems, we are given jobs and machines, and have to
schedule all the jobs to minimize some objective function. What if each job has
a specified profit, and we are no longer required to process all jobs -- we can
schedule any subset of jobs whose total profit is at least a (hard) target
profit requirement, while still approximately minimizing the objective
function?
We refer to this class of problems as scheduling with outliers. This model
was initiated by Charikar and Khuller (SODA'06) on the minimum max-response
time in broadcast scheduling. We consider three other well-studied scheduling
objectives: the generalized assignment problem, average weighted completion
time, and average flow time, and provide LP-based approximation algorithms for
them. For the minimum average flow time problem on identical machines, we give
a logarithmic approximation algorithm for the case of unit profits based on
rounding an LP relaxation; we also show a matching integrality gap. For the
average weighted completion time problem on unrelated machines, we give a
constant factor approximation. The algorithm is based on randomized rounding of
the time-indexed LP relaxation strengthened by the knapsack-cover inequalities.
For the generalized assignment problem with outliers, we give a simple
reduction to GAP without outliers to obtain an algorithm whose makespan is
within 3 times the optimum makespan, and whose cost is at most (1 + \epsilon)
times the optimal cost.Comment: 23 pages, 3 figure
Rogue-Instance Security for Batch Knowledge Proofs
We propose a new notion of knowledge soundness, denoted rogue-instance security, for interactive and non-interactive batch knowledge proofs. Our notion, inspired by the standard notion of rogue-key security for multi-signature schemes, considers a setting in which a malicious prover is provided with an honestly-generated instance , and may then be able to maliciously generate related rogue instances for convincing a verifier in a batch knowledge proof of corresponding witnesses for all instances - without actually having knowledge of the witness corresponding to the honestly-generated instance. This setting provides a powerful security guarantee for batch versions of a wide variety of practically-relevant protocols, such as Schnorr\u27s protocol and similar ones.
We present a highly-efficient generic construction of a batch proof-of-knowledge applicable to any algebraic Sigma protocols. The algebraic property refers to a homomorphic structure of the underlying group and includes Schnorr\u27s protocol and others. We provide an almost tight security analysis for our generic batch protocol, which significantly improves upon the previously known security bounds even for the specific case of batch Schnorr protocol. We extend our results beyond algebraic Sigma protocols. We analyze the rogue-instance security of a general batch protocol with plus-one special soundness (a generalization of standard special soundness) and achieve improved security bounds in the generic case.
Our results use a particular type of high-moment assumptions introduced by Rotem and Segev (CRYPTO 2021). These assumptions consider the hardness of a relation against algorithms with bounded expected running time. Although Rotem and Segev introduced these assumptions, they did not provide evidence to support their hardness. To substantiate and validate the high-moment assumptions, we present a new framework for assessing the concrete hardness of cryptographic problems against oracle algorithms with bounded expected runtime. Our framework covers generic models, including the generic group model, random oracle model, and more. Utilizing our framework, we achieve the first hardness result for these high-moment assumptions. In particular, we establish the second-moment hardness of the discrete-logarithm problem against expected-time algorithms in the generic group model
Subthreshold Voltage Noise Due to Channel Fluctuations in Active Neuronal Membranes
Voltage-gated ion channels in neuronal membranes fluctuate randomly between different conformational states due to thermal agitation. Fluctuations between conducting and nonconducting states give rise to noisy membrane currents and subthreshold voltage fluctuations and may contribute to variability in spike timing. Here we study subthreshold voltage fluctuations due to active voltage-gated Na+ and K+ channels as predicted by two commonly used kinetic schemes: the Mainen et al. (1995) (MJHS) kinetic scheme, which has been used to model dendritic channels in cortical neurons, and the classical Hodgkin-Huxley (1952) (HH) kinetic scheme for the squid giant axon. We compute the magnitudes, amplitude distributions, and power spectral densities of the voltage noise in isopotential membrane patches predicted by these kinetic schemes. For both schemes, noise magnitudes increase rapidly with depolarization from rest. Noise is larger for smaller patch areas but is smaller for increased model temperatures. We contrast the results from Monte Carlo simulations of the stochastic nonlinear kinetic schemes with analytical, closed-form expressions derived using passive and quasi-active linear approximations to the kinetic schemes. For all subthreshold voltage ranges, the quasi-active linearized approximation is accurate within 8% and may thus be used in large-scale simulations of realistic neuronal geometries
Hierarchical Functional Encryption
Functional encryption provides fine-grained access control for encrypted data, allowing each user to learn only specific functions of the encrypted data. We study the notion of hierarchical functional encryption, which augments functional encryption with delegation capabilities, offering significantly more expressive access control.
We present a generic transformation that converts any general-purpose public-key functional encryption scheme into a hierarchical one without relying on any additional assumptions. This significantly refines our understanding of the power of functional encryption, showing that the existence of functional encryption is equivalent to that of its hierarchical generalization.
Instantiating our transformation with the existing functional encryption schemes yields a variety of hierarchical schemes offering various trade-offs between their delegation capabilities (i.e., the depth and width of their hierarchical structures) and underlying assumptions. When starting with a scheme secure against an unbounded number of collusions, we can support arbitrary hierarchical structures. In addition, even when starting with schemes that are secure against a bounded number of collusions (which are known to exist under rather minimal assumptions such as the existence of public-key encryption and shallow pseudorandom generators), we can support hierarchical structures of bounded depth and width
Time-refraction and time-reflection above critical angle for total internal reflection
We study the time-reflection and time-refraction of waves caused by a spatial
interface with a medium undergoing a sudden temporal change in permittivity. We
show that monochromatic waves are transformed into a pulse by the permittivity
change, and that time-reflection is enhanced at the vicinity of the critical
angle for total internal reflection. In this regime, we find that the
evanescent field is transformed into a propagating pulse by the sudden change
in permittivity. These effects display enhancement of the time-reflection and
high sensitivity near the critical angle, paving the way to experiments on
time-reflection and photonic time-crystals at optical frequencies
Multiple State Electrostatically Formed Nanowire Transistors
This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Electrostatically Formed Nanowire (EFN) based transistors have been suggested in the past as gas sensing devices. These transistors are multiple gate transistors in which the source to drain conduction path is determined by the bias applied to the back gate, and two junction gates. If a specific bias is applied to the side gates, the conduction band electrons between them are confined to a well-defined area forming a narrow channel- the Electrostatically Formed Nanowire. Recent work has shown that by applying non-symmetric bias on the side gates, the lateral position of the EFN can be controlled. We propose a novel Multiple State EFN Transistor (MSET) that utilizes this degree of freedom for the implementation of complete multiplexer functionality in a single transistor like device. The multiplexer functionality allows a very simple implementation of binary and multiple valued logic functions
Weak pairwise correlations imply strongly correlated network states in a neural population
Biological networks have so many possible states that exhaustive sampling is
impossible. Successful analysis thus depends on simplifying hypotheses, but
experiments on many systems hint that complicated, higher order interactions
among large groups of elements play an important role. In the vertebrate
retina, we show that weak correlations between pairs of neurons coexist with
strongly collective behavior in the responses of ten or more neurons.
Surprisingly, we find that this collective behavior is described quantitatively
by models that capture the observed pairwise correlations but assume no higher
order interactions. These maximum entropy models are equivalent to Ising
models, and predict that larger networks are completely dominated by
correlation effects. This suggests that the neural code has associative or
error-correcting properties, and we provide preliminary evidence for such
behavior. As a first test for the generality of these ideas, we show that
similar results are obtained from networks of cultured cortical neurons.Comment: Full account of work presented at the conference on Computational and
Systems Neuroscience (COSYNE), 17-20 March 2005, in Salt Lake City, Utah
(http://cosyne.org
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