1,793 research outputs found
Computational Difficulty of Global Variations in the Density Matrix Renormalization Group
The density matrix renormalization group (DMRG) approach is arguably the most
successful method to numerically find ground states of quantum spin chains. It
amounts to iteratively locally optimizing matrix-product states, aiming at
better and better approximating the true ground state. To date, both a proof of
convergence to the globally best approximation and an assessment of its
complexity are lacking. Here we establish a result on the computational
complexity of an approximation with matrix-product states: The surprising
result is that when one globally optimizes over several sites of local
Hamiltonians, avoiding local optima, one encounters in the worst case a
computationally difficult NP-hard problem (hard even in approximation). The
proof exploits a novel way of relating it to binary quadratic programming. We
discuss intriguing ramifications on the difficulty of describing quantum
many-body systems.Comment: 5 pages, 1 figure, RevTeX, final versio
The Auto/paracrine regulation of endocrine functions: a history of TGF-β and the adrenal cortex
Aquesta breu revisió vol analitzar quinze anys de recerca que han portat a proposar el factor
de creixement transformant beta (TGF-β) com un component endogen auto/paracrí de la regulació
de les funcions diferenciades de teixits endocrins, com el còrtex adrenal. El TGF-β reuneix
els criteris requerits per aquesta funció, és a dir: a) El pèptid TGF-β està produït per les cèll. ules
adrenocorticals i expressat in situ en aquest teixit; b) el TGF-β reprimeix considerablement la
capacitat esteroidogènica d'aquestes cèll. ules reprimint els marcadors clau de diferenciació; c)
l'hormona sistèmica ACTH modula la resposta de les cèll. ules adrenocorticals al TGF-β; d) la
supressió de la síntesi de TGF-β suprimeix la inhibició de l'activitat esteroidogènica d'aquestes
cèll. ules. El sistema del TGF-β adrenocortical és, al nostre entendre, el primer circuit regulador
(loop) clarament establert en un teixit endocrí. Aquest viatge històric és un tribut al nostre amic
José Sáez, que va participar activament en el coneixement d'aquesta història.This brief review is intended as a flash-back spanning over fifteen years of research and finally
leading to the proposal that TGF-β could be an endogenous, auto/paracrine component in the
regulation of the differentiated functions of an endocrine tissue, i.e., the adrenal cortex. TGF-β
meets the criteria required for such a function: (i) the peptide is produced by adrenocortical
cells and expressed in the tissue in situ; (ii) TGF-β strikingly down-regulates the steroidogenic
capacity of these cells by repressing key differentiation markers; (iii) the systemic hormone
ACTH modulates the adrenocortical cells responsiveness to TGF-β, and (iv) the suppression
of TGF-β synthesis releases the inhibition of the steroidogenic activity of these cells. The TGF-β
adrenocortical cell system was, to our knowledge, the first autocrine regulatory loop clearly
established in an endocrine tissue. This chronological account is a tribute to our friend, José
Sáez, who actively contributed to this history
Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost
In a two-player game, two cooperating but non communicating players, Alice
and Bob, receive inputs taken from a probability distribution. Each of them
produces an output and they win the game if they satisfy some predicate on
their inputs/outputs. The entangled value of a game is the
maximum probability that Alice and Bob can win the game if they are allowed to
share an entangled state prior to receiving their inputs.
The -fold parallel repetition of consists of instances of
where the players receive all the inputs at the same time and produce all
the outputs at the same time. They win if they win each instance of .
In this paper we show that for any game such that , decreases exponentially in . First, for
any game on the uniform distribution, we show that , where and are the sizes of the input
and output sets. From this result, we show that for any entangled game ,
where is the input distribution of and
. This implies parallel
repetition with exponential decay as long as for
general games. To prove this parallel repetition, we introduce the concept of
\emph{Superposed Information Cost} for entangled games which is inspired from
the information cost used in communication complexity.Comment: In the first version of this paper we presented a different, stronger
Corollary 1 but due to an error in the proof we had to modify it in the
second version. This third version is a minor update. We correct some typos
and re-introduce a proof accidentally commented out in the second versio
Algorithmic and Hardness Results for the Colorful Components Problems
In this paper we investigate the colorful components framework, motivated by
applications emerging from comparative genomics. The general goal is to remove
a collection of edges from an undirected vertex-colored graph such that in
the resulting graph all the connected components are colorful (i.e., any
two vertices of the same color belong to different connected components). We
want to optimize an objective function, the selection of this function
being specific to each problem in the framework.
We analyze three objective functions, and thus, three different problems,
which are believed to be relevant for the biological applications: minimizing
the number of singleton vertices, maximizing the number of edges in the
transitive closure, and minimizing the number of connected components.
Our main result is a polynomial time algorithm for the first problem. This
result disproves the conjecture of Zheng et al. that the problem is -hard
(assuming ). Then, we show that the second problem is -hard,
thus proving and strengthening the conjecture of Zheng et al. that the problem
is -hard. Finally, we show that the third problem does not admit
polynomial time approximation within a factor of for
any , assuming (or within a factor of , assuming ).Comment: 18 pages, 3 figure
Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model
Motivated by applications such as viral marketing, the problem of influence
maximization (IM) has been extensively studied in the literature. The goal is
to select a small number of users to adopt an item such that it results in a
large cascade of adoptions by others. Existing works have three key
limitations. (1) They do not account for economic considerations of a user in
buying/adopting items. (2) Most studies on multiple items focus on competition,
with complementary items receiving limited attention. (3) For the network
owner, maximizing social welfare is important to ensure customer loyalty, which
is not addressed in prior work in the IM literature. In this paper, we address
all three limitations and propose a novel model called UIC that combines
utility-driven item adoption with influence propagation over networks. Focusing
on the mutually complementary setting, we formulate the problem of social
welfare maximization in this novel setting. We show that while the objective
function is neither submodular nor supermodular, surprisingly a simple greedy
allocation algorithm achieves a factor of of the optimum
expected social welfare. We develop \textsf{bundleGRD}, a scalable version of
this approximation algorithm, and demonstrate, with comprehensive experiments
on real and synthetic datasets, that it significantly outperforms all
baselines.Comment: 33 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
Replica Placement on Bounded Treewidth Graphs
We consider the replica placement problem: given a graph with clients and
nodes, place replicas on a minimum set of nodes to serve all the clients; each
client is associated with a request and maximum distance that it can travel to
get served and there is a maximum limit (capacity) on the amount of request a
replica can serve. The problem falls under the general framework of capacitated
set covering. It admits an O(\log n)-approximation and it is NP-hard to
approximate within a factor of . We study the problem in terms of
the treewidth of the graph and present an O(t)-approximation algorithm.Comment: An abridged version of this paper is to appear in the proceedings of
WADS'1
On the Design of Cryptographic Primitives
The main objective of this work is twofold. On the one hand, it gives a brief
overview of the area of two-party cryptographic protocols. On the other hand,
it proposes new schemes and guidelines for improving the practice of robust
protocol design. In order to achieve such a double goal, a tour through the
descriptions of the two main cryptographic primitives is carried out. Within
this survey, some of the most representative algorithms based on the Theory of
Finite Fields are provided and new general schemes and specific algorithms
based on Graph Theory are proposed
Budget-restricted utility games with ordered strategic decisions
We introduce the concept of budget games. Players choose a set of tasks and
each task has a certain demand on every resource in the game. Each resource has
a budget. If the budget is not enough to satisfy the sum of all demands, it has
to be shared between the tasks. We study strategic budget games, where the
budget is shared proportionally. We also consider a variant in which the order
of the strategic decisions influences the distribution of the budgets. The
complexity of the optimal solution as well as existence, complexity and quality
of equilibria are analyzed. Finally, we show that the time an ordered budget
game needs to convergence towards an equilibrium may be exponential
Implementation of higher-order absorbing boundary conditions for the Einstein equations
We present an implementation of absorbing boundary conditions for the
Einstein equations based on the recent work of Buchman and Sarbach. In this
paper, we assume that spacetime may be linearized about Minkowski space close
to the outer boundary, which is taken to be a coordinate sphere. We reformulate
the boundary conditions as conditions on the gauge-invariant
Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated
by rewriting the boundary conditions as a system of ODEs for a set of auxiliary
variables intrinsic to the boundary. From these we construct boundary data for
a set of well-posed constraint-preserving boundary conditions for the Einstein
equations in a first-order generalized harmonic formulation. This construction
has direct applications to outer boundary conditions in simulations of isolated
systems (e.g., binary black holes) as well as to the problem of
Cauchy-perturbative matching. As a test problem for our numerical
implementation, we consider linearized multipolar gravitational waves in TT
gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We
demonstrate that the perfectly absorbing boundary condition B_L of order L=l
yields no spurious reflections to linear order in perturbation theory. This is
in contrast to the lower-order absorbing boundary conditions B_L with L<l,
which include the widely used freezing-Psi_0 boundary condition that imposes
the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in
Class. Quantum Grav
- …