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Mental Imagery and Chunks: Empirical and Computational Findings
To investigate experts’ imagery in chess, players were required to recall briefly-presented positions in which the pieces were placed on the intersections between squares (intersection positions). Position types ranged from game positions to positions where both the piece distribution and location were randomized. Simulations were run with the CHREST model (Gobet & Simon, 2000). The simulations assumed that pieces had to be centered back one by one to the middle of the squares in the mind’s eye before chunks could be recognized. Consistent with CHREST’s predictions, chess players (N = 36), ranging from weak amateurs to grandmasters, exhibited much poorer recall on intersection positions than on standard positions (pieces placed on centers of squares). On the intersection positions, the skill difference in recall was larger on game positions than on the randomized positions. Participants recalled bishops better than knights, suggesting that Stroop-like interference impairs recall of the latter. The data supported both the time parameter in CHREST for shifting pieces in the mind’s eye (125 ms per piece) and the seriality assumption. In general, the study reinforces the plausibility of CHREST as a model of cognition
Constrained distributed optimization : A population dynamics approach
Large-scale network systems involve a large number of states, which makes the design of real-time controllers a challenging task. A distributed controller design allows to reduce computational requirements since tasks are divided into different systems, allowing real-time processing. This paper proposes a novel methodology for solving constrained optimization problems in a distributed way inspired by population dynamics. This methodology consists of an extension of a population dynamics equation and the introduction of a mass dynamics equation. The proposed methodology divides the problem into smaller sub-problems, whose feasible regions vary over time achieving an agreement to solve the global problem. The methodology also guarantees attraction to the feasible region and allows to have few changes in the decision-making design when a network suffers the addition/removal of nodes/edges. Then, distributed controllers are designed with the proposed methodology and applied to the large-scale Barcelona Drinking Water Network (BDWN). Some simulations are presented and discussed in order to illustrate the control performance.Peer ReviewedPostprint (author's final draft
Models of discretized moduli spaces, cohomological field theories, and Gaussian means
We prove combinatorially the explicit relation between genus filtrated
-loop means of the Gaussian matrix model and terms of the genus expansion of
the Kontsevich--Penner matrix model (KPMM). The latter is the generating
function for volumes of discretized (open) moduli spaces
given by for
. This generating function therefore enjoys
the topological recursion, and we prove that it is simultaneously the
generating function for ancestor invariants of a cohomological field theory
thus enjoying the Givental decomposition. We use another Givental-type
decomposition obtained for this model by the second authors in 1995 in terms of
special times related to the discretisation of moduli spaces thus representing
its asymptotic expansion terms (and therefore those of the Gaussian means) as
finite sums over graphs weighted by lower-order monomials in times thus giving
another proof of (quasi)polynomiality of the discrete volumes. As an
application, we find the coefficients in the first subleading order for
in two ways: using the refined Harer--Zagier recursion and
by exploiting the above Givental-type transformation. We put forward the
conjecture that the above graph expansions can be used for probing the
reduction structure of the Delgne--Mumford compactification of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure
On the Complexity of Spill Everywhere under SSA Form
Compilation for embedded processors can be either aggressive (time consuming
cross-compilation) or just in time (embedded and usually dynamic). The
heuristics used in dynamic compilation are highly constrained by limited
resources, time and memory in particular. Recent results on the SSA form open
promising directions for the design of new register allocation heuristics for
embedded systems and especially for embedded compilation. In particular,
heuristics based on tree scan with two separated phases -- one for spilling,
then one for coloring/coalescing -- seem good candidates for designing
memory-friendly, fast, and competitive register allocators. Still, also because
of the side effect on power consumption, the minimization of loads and stores
overhead (spilling problem) is an important issue. This paper provides an
exhaustive study of the complexity of the ``spill everywhere'' problem in the
context of the SSA form. Unfortunately, conversely to our initial hopes, many
of the questions we raised lead to NP-completeness results. We identify some
polynomial cases but that are impractical in JIT context. Nevertheless, they
can give hints to simplify formulations for the design of aggressive
allocators.Comment: 10 page
Low-Energy Analysis of and Theories on Calabi-Yau Threefolds
We elucidate the interplay between gauge and supersymmetry anomalies in
six-dimensional supergravity with generalized couplings between tensor
and vector multiplets. We derive the structure of the five-dimensional
supergravity resulting from the reduction of these models and give the
constraints on Chern-Simons couplings that follow from duality to theory
compactified on a Calabi-Yau threefold. The duality is supported only on a
restricted class of Calabi-Yau threefolds and requires a special type of
intersection form. We derive five-dimensional central-charge formulas and
discuss briefly the associated phase transitions. Finally, we exhibit
connections with -theory compactifications on Calabi-Yau manifolds that
admit elliptic fibrations. This analysis suggests that theory unifies
Type- three-branes and -theory five-branes.Comment: 27 pages, LaTex. final version, to appear in Nucl. Phys.
Low-Complexity OFDM Spectral Precoding
This paper proposes a new large-scale mask-compliant spectral precoder
(LS-MSP) for orthogonal frequency division multiplexing systems. In this paper,
we first consider a previously proposed mask-compliant spectral precoding
scheme that utilizes a generic convex optimization solver which suffers from
high computational complexity, notably in large-scale systems. To mitigate the
complexity of computing the LS-MSP, we propose a divide-and-conquer approach
that breaks the original problem into smaller rank 1 quadratic-constraint
problems and each small problem yields closed-form solution. Based on these
solutions, we develop three specialized first-order low-complexity algorithms,
based on 1) projection on convex sets and 2) the alternating direction method
of multipliers. We also develop an algorithm that capitalizes on the
closed-form solutions for the rank 1 quadratic constraints, which is referred
to as 3) semi-analytical spectral precoding. Numerical results show that the
proposed LS-MSP techniques outperform previously proposed techniques in terms
of the computational burden while complying with the spectrum mask. The results
also indicate that 3) typically needs 3 iterations to achieve similar results
as 1) and 2) at the expense of a slightly increased computational complexity.Comment: Accepted in IEEE International Workshop on Signal Processing Advances
in Wireless Communications (SPAWC), 201
Mechanism Design via Correlation Gap
For revenue and welfare maximization in single-dimensional Bayesian settings,
Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms
(SPMs), though simple in form, can perform surprisingly well compared to the
optimal mechanisms. In this paper, we give a theoretical explanation of this
fact, based on a connection to the notion of correlation gap.
Loosely speaking, for auction environments with matroid constraints, we can
relate the performance of a mechanism to the expectation of a monotone
submodular function over a random set. This random set corresponds to the
winner set for the optimal mechanism, which is highly correlated, and
corresponds to certain demand set for SPMs, which is independent. The notion of
correlation gap of Agrawal et al.\ (SODA10) quantifies how much we {}"lose" in
the expectation of the function by ignoring correlation in the random set, and
hence bounds our loss in using certain SPM instead of the optimal mechanism.
Furthermore, the correlation gap of a monotone and submodular function is known
to be small, and it follows that certain SPM can approximate the optimal
mechanism by a good constant factor.
Exploiting this connection, we give tight analysis of a greedy-based SPM of
Chawla et al.\ for several environments. In particular, we show that it gives
an -approximation for matroid environments, gives asymptotically a
-approximation for the important sub-case of -unit
auctions, and gives a -approximation for environments with
-independent set system constraints
Understanding Predication in Conceptual Spaces
We argue that a cognitive semantics has to take into account the possibly
partial information that a cognitive agent has of the world. After discussing
Gärdenfors's view of objects in conceptual spaces, we offer a number of viable
treatments of partiality of information and we formalize them by means of alternative
predicative logics. Our analysis shows that understanding the nature of simple
predicative sentences is crucial for a cognitive semantics
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