963 research outputs found
From average case complexity to improper learning complexity
The basic problem in the PAC model of computational learning theory is to
determine which hypothesis classes are efficiently learnable. There is
presently a dearth of results showing hardness of learning problems. Moreover,
the existing lower bounds fall short of the best known algorithms.
The biggest challenge in proving complexity results is to establish hardness
of {\em improper learning} (a.k.a. representation independent learning).The
difficulty in proving lower bounds for improper learning is that the standard
reductions from -hard problems do not seem to apply in this
context. There is essentially only one known approach to proving lower bounds
on improper learning. It was initiated in (Kearns and Valiant 89) and relies on
cryptographic assumptions.
We introduce a new technique for proving hardness of improper learning, based
on reductions from problems that are hard on average. We put forward a (fairly
strong) generalization of Feige's assumption (Feige 02) about the complexity of
refuting random constraint satisfaction problems. Combining this assumption
with our new technique yields far reaching implications. In particular,
1. Learning 's is hard.
2. Agnostically learning halfspaces with a constant approximation ratio is
hard.
3. Learning an intersection of halfspaces is hard.Comment: 34 page
Universal Protocols for Information Dissemination Using Emergent Signals
We consider a population of agents which communicate with each other in a
decentralized manner, through random pairwise interactions. One or more agents
in the population may act as authoritative sources of information, and the
objective of the remaining agents is to obtain information from or about these
source agents. We study two basic tasks: broadcasting, in which the agents are
to learn the bit-state of an authoritative source which is present in the
population, and source detection, in which the agents are required to decide if
at least one source agent is present in the population or not.We focus on
designing protocols which meet two natural conditions: (1) universality, i.e.,
independence of population size, and (2) rapid convergence to a correct global
state after a reconfiguration, such as a change in the state of a source agent.
Our main positive result is to show that both of these constraints can be met.
For both the broadcasting problem and the source detection problem, we obtain
solutions with a convergence time of rounds, w.h.p., from any
starting configuration. The solution to broadcasting is exact, which means that
all agents reach the state broadcast by the source, while the solution to
source detection admits one-sided error on a -fraction of the
population (which is unavoidable for this problem). Both protocols are easy to
implement in practice and have a compact formulation.Our protocols exploit the
properties of self-organizing oscillatory dynamics. On the hardness side, our
main structural insight is to prove that any protocol which meets the
constraints of universality and of rapid convergence after reconfiguration must
display a form of non-stationary behavior (of which oscillatory dynamics are an
example). We also observe that the periodicity of the oscillatory behavior of
the protocol, when present, must necessarily depend on the number ^\\# X of
source agents present in the population. For instance, our protocols inherently
rely on the emergence of a signal passing through the population, whose period
is \Theta(\log \frac{n}{^\\# X}) rounds for most starting configurations. The
design of clocks with tunable frequency may be of independent interest, notably
in modeling biological networks
New Approximability Results for the Robust k-Median Problem
We consider a robust variant of the classical -median problem, introduced
by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust -Median problem},
we are given an -vertex metric space and client sets . The objective is to open a set of
facilities such that the worst case connection cost over all client sets is
minimized; in other words, minimize . Anthony
et al.\ showed an approximation algorithm for any metric and
APX-hardness even in the case of uniform metric. In this paper, we show that
their algorithm is nearly tight by providing
approximation hardness, unless . This hardness result holds even for uniform and line
metrics. To our knowledge, this is one of the rare cases in which a problem on
a line metric is hard to approximate to within logarithmic factor. We
complement the hardness result by an experimental evaluation of different
heuristics that shows that very simple heuristics achieve good approximations
for realistic classes of instances.Comment: 19 page
Role of EG-VEGF in Human Placentation: Physiological and Pathological Implications
International audienc
Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines
We consider the problem of scheduling jobs on unrelated machines so as to
minimize the sum of weighted completion times. Our main result is a
-approximation algorithm for some fixed , improving upon the
long-standing bound of 3/2 (independently due to Skutella, Journal of the ACM,
2001, and Sethuraman & Squillante, SODA, 1999). To do this, we first introduce
a new lift-and-project based SDP relaxation for the problem. This is necessary
as the previous convex programming relaxations have an integrality gap of
. Second, we give a new general bipartite-rounding procedure that produces
an assignment with certain strong negative correlation properties.Comment: 21 pages, 4 figure
The Corepressor NCoR1 Antagonizes PGC-1α and Estrogen-Related Receptor α in the Regulation of Skeletal Muscle Function and Oxidative Metabolism
Skeletal muscle exhibits a high plasticity and accordingly can quickly adapt to different physiological and pathological stimuli by changing its phenotype largely through diverse epigenetic mechanisms. The nuclear receptor corepressor 1 (NCoR1) has the ability to mediate gene repression; however, its role in regulating biological programs in skeletal muscle is still poorly understood. We therefore studied the mechanistic and functional aspects of NCoR1 function in this tissue. NCoR1 muscle-specific knockout mice exhibited a 7.2% higher peak oxygen consumption (VO(2peak)), a 11% reduction in maximal isometric force, and increased ex vivo fatigue resistance during maximal stimulation. Interestingly, global gene expression analysis revealed a high overlap between the effects of NCoR1 deletion and peroxisome proliferator-activated receptor gamma (PPARγ) coactivator 1α (PGC-1α) overexpression on oxidative metabolism in muscle. Importantly, PPARβ/δ and estrogen-related receptor α (ERRα) were identified as common targets of NCoR1 and PGC-1α with opposing effects on the transcriptional activity of these nuclear receptors. In fact, the repressive effect of NCoR1 on oxidative phosphorylation gene expression specifically antagonizes PGC-1α-mediated coactivation of ERRα. We therefore delineated the molecular mechanism by which a transcriptional network controlled by corepressor and coactivator proteins determines the metabolic properties of skeletal muscle, thus representing a potential therapeutic target for metabolic diseases
Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure
We study the problem of finding and characterizing subgraphs with small
\textit{bipartiteness ratio}. We give a bicriteria approximation algorithm
\verb|SwpDB| such that if there exists a subset of volume at most and
bipartiteness ratio , then for any , it finds a set
of volume at most and bipartiteness ratio at most
. By combining a truncation operation, we give a local
algorithm \verb|LocDB|, which has asymptotically the same approximation
guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness
ratio of the output set, and runs in time
, independent of the size of the
graph. Finally, we give a spectral characterization of the small dense
bipartite-like subgraphs by using the th \textit{largest} eigenvalue of the
Laplacian of the graph.Comment: 17 pages; ISAAC 201
Reoptimization of Some Maximum Weight Induced Hereditary Subgraph Problems
The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π, an optimal solution OPT for Π in I and an instance I′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I', either optimally or by guaranteeing an approximation ratio better than that guaranteed by an ex nihilo computation and with running time better than that needed for such a computation. We use this setting in order to study weighted versions of several representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. The main problems studied are max independent set, max k-colorable subgraph and max split subgraph under vertex insertions and deletion
Random Tensors and Planted Cliques
The r-parity tensor of a graph is a generalization of the adjacency matrix,
where the tensor's entries denote the parity of the number of edges in
subgraphs induced by r distinct vertices. For r=2, it is the adjacency matrix
with 1's for edges and -1's for nonedges. It is well-known that the 2-norm of
the adjacency matrix of a random graph is O(\sqrt{n}). Here we show that the
2-norm of the r-parity tensor is at most f(r)\sqrt{n}\log^{O(r)}n, answering a
question of Frieze and Kannan who proved this for r=3. As a consequence, we get
a tight connection between the planted clique problem and the problem of
finding a vector that approximates the 2-norm of the r-parity tensor of a
random graph. Our proof method is based on an inductive application of
concentration of measure
Integrating nuclear receptor mobility in models of gene regulation
The mode of action of nuclear receptors in living cells is an actively investigated field but much remains hypothetical due to the lack, until recently, of methods allowing the assessment of molecular mechanisms in vivo. However, these last years, the development of fluorescence microscopy methods has allowed initiating the dissection of the molecular mechanisms underlying gene regulation by nuclear receptors directly in living cells or organisms. Following our analyses on peroxisome proliferator activated receptors (PPARs) in living cells, we discuss here the different models arising from the use of these tools, that attempt to link mobility, DNA binding or chromatin interaction, and transcriptional activity
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