6,662 research outputs found
Sharp nonasymptotic bounds on the norm of random matrices with independent entries
We obtain nonasymptotic bounds on the spectral norm of random matrices with
independent entries that improve significantly on earlier results. If is
the symmetric matrix with , we show that
This bound is optimal in the sense that a matching
lower bound holds under mild assumptions, and the constants are sufficiently
sharp that we can often capture the precise edge of the spectrum. Analogous
results are obtained for rectangular matrices and for more general sub-Gaussian
or heavy-tailed distributions of the entries, and we derive tail bounds in
addition to bounds on the expected norm. The proofs are based on a combination
of the moment method and geometric functional analysis techniques. As an
application, we show that our bounds immediately yield the correct phase
transition behavior of the spectral edge of random band matrices and of sparse
Wigner matrices. We also recover a result of Seginer on the norm of Rademacher
matrices.Comment: Published at http://dx.doi.org/10.1214/15-AOP1025 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs
We study the representation theory of a certain finite group for which
Kloosterman sums appear as character values. This leads us to consider a
concrete family of commuting hermitian matrices which have Kloosterman sums as
eigenvalues. These matrices satisfy a number of "magical" combinatorial
properties and they encode various arithmetic properties of Kloosterman sums.
These matrices can also be regarded as adjacency matrices for multigraphs which
display Ramanujan-like behavior.Comment: 20 page
Formal Scheduling Constraints for Time-Sensitive Networks
In recent years, the IEEE 802.1 Time Sensitive Networking (TSN) task group
has been active standardizing time-sensitive capabilities for Ethernet networks
ranging from distributed clock synchronization and time-based ingress policing
to frame preemption, redundancy management, and scheduled traffic enhancements.
In particular the scheduled traffic enhancements defined in IEEE 802.1Qbv
together with the clock synchronization protocol open up the possibility to
schedule communication in distributed networks providing real-time guarantees.
In this paper we formalize the necessary constraints for creating
window-based IEEE~802.1Qbv Gate Control List schedules for Time-sensitive
Networks (TSN). The resulting schedules allow a greater flexibility in terms of
timing properties while still guaranteeing deterministic communication with
bounded jitter and end-to-end latency
Musical Actions of Dihedral Groups
The sequence of pitches which form a musical melody can be transposed or
inverted. Since the 1970s, music theorists have modeled musical transposition
and inversion in terms of an action of the dihedral group of order 24. More
recently music theorists have found an intriguing second way that the dihedral
group of order 24 acts on the set of major and minor chords. We illustrate both
geometrically and algebraically how these two actions are {\it dual}. Both
actions and their duality have been used to analyze works of music as diverse
as Hindemith and the Beatles.Comment: 27 pages, 11 figures. To appear in the American Mathematical Monthly
Ensuring a More Evidence-based Policy for Basic Education
Can the Philippines achieve its goal on two key international commitments--the Millennium Development Goals (MDGs) on Education and the Education for All (EFA) Initiative--for the achievement of education for everyone? A closer look at the figures would show that the country may be at risk of not achieving its goal of attaining universal primary education by 2015. Given this scenario, the authors suggest that the government should intensify its efforts in improving basic education by having evidence-based policies and actions. In particular, they note that the Department of Education (DepEd) should be required to have a sound monitoring and evaluation system to regularly assess the conditions of basic education.basic education, millennium development goal (MDG), education indicators, monitoring and evaluation
On the nature of the AGILE galactic transient sources
The Italian gamma-ray satellite AGILE has recently reported the detection of
some variable high-energy sources likely of galactic origin. These sources do
not have any obvious counterpart at lower energies. We propose that these
sources are produced in proton-dominated jets of galactic microquasars. We
develop a model for microquasar jets that takes into account both primary
leptons and protons and all relevant radiative processes, including secondary
particle emission and gamma-ray attenuation due to pair creation in the jet. We
obtain spectral energy distributions that correspond to what is observed by
AGILE, with most of the power concentrated between 100 MeV and 10 GeV and
reaching luminosities of erg s. We make detailed spectral
predictions that can be tested by the Fermi gamma-ray telescope in the
immediate future. We conclude that hadronic jets in galactic accreting sources
can be responsible for the variable unidentified gamma-ray sources detected by
AGILE.Comment: 4 pages, 2 figures. Accepted for publication in Astronomy &
Astrophysics (Letters
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