14,210 research outputs found
Ihara zeta functions for periodic simple graphs
The definition and main properties of the Ihara zeta function for graphs are
reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we
give a new proof of the associated determinant formula, based on the treatment
developed by Stark and Terras for finite graphs.Comment: 17 pages, 7 figures. V3: minor correction
A trace on fractal graphs and the Ihara zeta function
Starting with Ihara's work in 1968, there has been a growing interest in the
study of zeta functions of finite graphs, by Sunada, Hashimoto, Bass, Stark and
Terras, Mizuno and Sato, to name just a few authors. Then, Clair and
Mokhtari-Sharghi have studied zeta functions for infinite graphs acted upon by
a discrete group of automorphisms. The main formula in all these treatments
establishes a connection between the zeta function, originally defined as an
infinite product, and the Laplacian of the graph. In this article, we consider
a different class of infinite graphs. They are fractal graphs, i.e. they enjoy
a self-similarity property. We define a zeta function for these graphs and,
using the machinery of operator algebras, we prove a determinant formula, which
relates the zeta function with the Laplacian of the graph. We also prove
functional equations, and a formula which allows approximation of the zeta
function by the zeta functions of finite subgraphs.Comment: 30 pages, 5 figures. v3: minor corrections, to appear on Transactions
AM
Revisiting Shared Data Protection Against Key Exposure
This paper puts a new light on secure data storage inside distributed
systems. Specifically, it revisits computational secret sharing in a situation
where the encryption key is exposed to an attacker. It comes with several
contributions: First, it defines a security model for encryption schemes, where
we ask for additional resilience against exposure of the encryption key.
Precisely we ask for (1) indistinguishability of plaintexts under full
ciphertext knowledge, (2) indistinguishability for an adversary who learns: the
encryption key, plus all but one share of the ciphertext. (2) relaxes the
"all-or-nothing" property to a more realistic setting, where the ciphertext is
transformed into a number of shares, such that the adversary can't access one
of them. (1) asks that, unless the user's key is disclosed, noone else than the
user can retrieve information about the plaintext. Second, it introduces a new
computationally secure encryption-then-sharing scheme, that protects the data
in the previously defined attacker model. It consists in data encryption
followed by a linear transformation of the ciphertext, then its fragmentation
into shares, along with secret sharing of the randomness used for encryption.
The computational overhead in addition to data encryption is reduced by half
with respect to state of the art. Third, it provides for the first time
cryptographic proofs in this context of key exposure. It emphasizes that the
security of our scheme relies only on a simple cryptanalysis resilience
assumption for blockciphers in public key mode: indistinguishability from
random, of the sequence of diferentials of a random value. Fourth, it provides
an alternative scheme relying on the more theoretical random permutation model.
It consists in encrypting with sponge functions in duplex mode then, as before,
secret-sharing the randomness
Full control of qubit rotations in a voltage-biased superconducting flux qubit
We study a voltage-controlled version of the superconducting flux qubit
[Chiorescu et al., Science 299, 1869 (2003)] and show that full control of
qubit rotations on the entire Bloch sphere can be achieved. Circuit graph
theory is used to study a setup where voltage sources are attached to the two
superconducting islands formed between the three Josephson junctions in the
flux qubit. Applying a voltage allows qubit rotations about the y axis, in
addition to pure x and z rotations obtained in the absence of applied voltages.
The orientation and magnitude of the rotation axis on the Bloch sphere can be
tuned by the gate voltages, the external magnetic flux, and the ratio alpha
between the Josephson energies via a flux-tunable junction. We compare the
single-qubit control in the known regime alpha<1 with the unexplored range
alpha>1 and estimate the decoherence due to voltage fluctuations.Comment: 12 pages, 12 figures, 1 tabl
Why do emerging economies borrow short term?
We argue that one reason why emerging economies borrow short term is that it is cheaper than borrowing long term. This is especially the case during crises, as in these episodes the relative cost of long-term borrowing increases. We construct a unique database of sovereign bond prices, returns, and issuances at di¤erent maturities for 11 emerging economies from 1990 to 2009 and present a set of new stylized facts. On average, these countries pay a higher risk premium on long-term than on short-term bonds. During crises, the di¤erence between the two risk premia increases and issuance shifts towards shorter maturities. To illustrate our argument, we present a simple model in which the maturity structure is the outcome of a risk sharing problem between an emerging economy subject to rollover crises and risk averse international investors.emerging markets; debt crises; investor risk aversion; maturity structure; risk premium; term premium
Projections and Dyadic Parseval Frame MRA Wavelets
A classical theorem attributed to Naimark states that, given a Parseval frame
in a Hilbert space , one can embed in
a larger Hilbert space so that the image of is the
projection of an orthonormal basis for . In the present work, we
revisit the notion of Parseval frame MRA wavelets from two papers of
Paluszy\'nski, \v{S}iki\'c, Weiss, and Xiao (PSWX) and produce an analog of
Naimark's theorem for these wavelets at the level of their scaling functions.
We aim to make this discussion as self-contained as possible and provide a
different point of view on Parseval frame MRA wavelets than that of PSWX.Comment: 19 page
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