7,314 research outputs found
Analysis of overfitting in the regularized Cox model
The Cox proportional hazards model is ubiquitous in the analysis of
time-to-event data. However, when the data dimension p is comparable to the
sample size , maximum likelihood estimates for its regression parameters are
known to be biased or break down entirely due to overfitting. This prompted the
introduction of the so-called regularized Cox model. In this paper we use the
replica method from statistical physics to investigate the relationship between
the true and inferred regression parameters in regularized multivariate Cox
regression with L2 regularization, in the regime where both p and N are large
but with p/N ~ O(1). We thereby generalize a recent study from maximum
likelihood to maximum a posteriori inference. We also establish a relationship
between the optimal regularization parameter and p/N, allowing for
straightforward overfitting corrections in time-to-event analysis
Discrete Symmetries (C,P,T) in Noncommutative Field Theories
In this paper we study the invariance of the noncmmutative gauge theories
under C, P and T transformations. For the noncommutative space (when only the
spatial part of is non-zero) we show that NCQED is Parity invariant.
In addition, we show that under charge conjugation the theory on noncommutative
is transformed to the theory on , so NCQED is a
CP violating theory. The theory remains invariant under time reversal if,
together with proper changes in fields, we also change by .
Hence altogether NCQED is CPT invariant. Moreover we show that the CPT
invariance holds for general noncommutative space-time.Comment: Revtex File, 4 pages, no figures, minor changes from previous verion.
To appear in Phys. Rev. Let
Use of Mental Imagery in Psychotherapy: A Critical Review
The paper presents arguments in favor of the use of mental imagery for therapeutic purposes. Several existing imagery approaches to psychotherapy are critically examined and suggestions for future inquiry are offered. The intimate relation between imagery and the affective-somatic processes is stressed
Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM
We study near-horizon limits of near-extremal charged black hole solutions to
five-dimensional gauged supergravity carrying two charges, extending
the recent work of Balasubramanian et.al. We show that there are two
near-horizon decoupling limits for the near-extremal black holes, one
corresponding to the near-BPS case and the other for the far from BPS case.
Both of these limits are only defined on the 10d IIB uplift of the 5d black
holes, resulting in a decoupled geometry with a six-dimensional part (conformal
to) a rotating BTZ X . We study various aspects of these decoupling limits
both from the gravity side and the dual field theory side. For the latter we
argue that there should be two different, but equivalent, dual gauge theory
descriptions, one in terms of the 2d CFT's dual to the rotating BTZ and the
other as certain large R-charge sectors of d=4,N =4 U(N) SYM theory. We discuss
new BMN-type sectors of the N=4 SYM in the limit in which the
engineering dimensions scale as (for the near-BPS case) and as
(for the far from BPS case).Comment: 44 pages, references added, minor change
Measuring emission coordinates in a pulsar-based relativistic positioning system
A relativistic deep space positioning system has been proposed using four or
more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed
repetition period in its rest frame.) The positioning system uses the fact that
an event in spacetime can be fully described by emission coordinates: the
proper emission time of each pulse measured at the event. The proper emission
time of each pulse from four different pulsars---interpolated as
necessary---provides the four spacetime coordinates of the reception event in
the emission coordinate system. If more than four pulsars are available, the
redundancy can improve the accuracy of the determination and/or resolve
degeneracies resulting from special geometrical arrangements of the sources and
the event.
We introduce a robust numerical approach to measure the emission coordinates
of an event in any arbitrary spacetime geometry. Our approach uses a continuous
solution of the eikonal equation describing the backward null cone from the
event. The pulsar proper time at the instant the null cone intersects the
pulsar world line is one of the four required coordinates. The process is
complete (modulo degeneracies) when four pulsar world lines have been crossed
by the light cone.
The numerical method is applied in two different examples: measuring emission
coordinates of an event in Minkowski spacetime using pulses from four pulsars
stationary in the spacetime; and measuring emission coordinates of an event in
Schwarzschild spacetime using pulses from four pulsars freely falling toward a
static black hole.
These numerical simulations are merely exploratory, but with improved
resolution and computational resources the method can be applied to more
pertinent problems. For instance one could measure the emission coordinates,
and therefore the trajectory, of the Earth.Comment: 9 pages, 2 figures, v3: replaced with version accepted by Phys. Rev.
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