3,828 research outputs found
Sparse Hopfield network reconstruction with regularization
We propose an efficient strategy to infer sparse Hopfield network based on
magnetizations and pairwise correlations measured through Glauber samplings.
This strategy incorporates the regularization into the Bethe
approximation by a quadratic approximation to the log-likelihood, and is able
to further reduce the inference error of the Bethe approximation without the
regularization. The optimal regularization parameter is observed to be of the
order of where is the number of independent samples. The value
of the scaling exponent depends on the performance measure.
for root mean squared error measure while for
misclassification rate measure. The efficiency of this strategy is demonstrated
for the sparse Hopfield model, but the method is generally applicable to other
diluted mean field models. In particular, it is simple in implementation
without heavy computational cost.Comment: 9 pages, 3 figures, Eur. Phys. J. B (in press
Speculation in Standard Auctions with Resale
According to the theory of incomplete contracts, given nonverifiable entrepreneurial project choices together with divergent objectives between an entrepreneur and its outside financier, the entrepreneur can credibly pledge only part of its project outcome for external funding. Meanwhile, entrepreneurial net worth must be put as down payment to ameliorate agency costs. In a real dynamic general equilibrium model with heterogeneous agents and nonverifiable project choices, endogenous agency costs significantly change the businesscycle pattern in the sense that the model can replicate an important empirical fact, the amplified hump-shaped output behavior. Furthermore, variable asset prices can a ect entrepreneurial net worth and then subsequently change the dynamic features of aggregate output along business cycles.Asset Prices, Business Cycles, Credit Constraints, Hump-Shaped Output Dynamics, Nonverifiable Project Choice
Double Shuffle Relations of Double Zeta Values and Double Eisenstein Series of Level N
In their seminal paper "Double zeta values and modular forms" Gangl, Kaneko
and Zagier defined a double Eisenstein series and used it to study the
relations between double zeta values. One of their key ideas is to study the
formal double space and apply the double shuffle relations. They also proved
the double shuffle relations for the double Eisenstein series. More recently,
Kaneko and Tasaka extended the double Eisenstein series to level 2, proved its
double shuffle relations and studied the double zeta values of level 2.
Motivated by the above works, we define in this paper the corresponding objects
at higher levels and prove that the double Eisenstein series of level N
satisfies the double shuffle relations for every positive integer N. In order
to obtain our main theorem we prove a key result on the multiple divisor
functions of level N and then use it to solve a complicated under-determined
system of linear equations by some standard techniques from linear algebra.Comment: A new section 5 is added and a new Theorem 6.5 is prove
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