1,803 research outputs found
Geometric Analysis of Particular Compactly Constructed Time Machine Spacetimes
We formulate the concept of time machine structure for spacetimes exhibiting
a compactely constructed region with closed timelike curves. After reviewing
essential properties of the pseudo Schwarzschild spacetime introduced by A.
Ori, we present an analysis of its geodesics analogous to the one conducted in
the case of the Schwarzschild spacetime. We conclude that the pseudo
Schwarzschild spacetime is geodesically incomplete and not extendible to a
complete spacetime. We then introduce a rotating generalization of the pseudo
Schwarzschild metric, which we call the the pseudo Kerr spacetime. We establish
its time machine structure and analyze its global properties.Comment: 14 pages, 3 figure
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Psychosocial treatments for negative symptoms in schizophrenia: current practices and future directions.
Schizophrenia can be a chronic and debilitating psychiatric disorder. Though advancements have been made in the psychosocial treatment of some symptoms of schizophrenia, people with schizophrenia often continue to experience some level of symptoms, particularly negative symptoms, throughout their lives. Because negative symptoms are associated with poor functioning and quality of life, the treatment of negative symptoms is a high priority for intervention development. However, current psychosocial treatments primarily focus on the reduction of positive symptoms with comparatively few studies investigating the efficacy of psychosocial treatments for negative symptoms. In this article, we review and evaluate the existing literature on three categories of psychosocial treatments--cognitive behavioral therapy (CBT), social skills training (SST), and combined treatment interventions--and their impact on the negative symptoms of schizophrenia. Of the interventions reviewed, CBT and SST appear to have the most empirical support, with some evidence suggesting that CBT is associated with maintenance of negative symptom improvement beyond six months after treatment. It remains unclear if a combined treatment approach provides improvements above and beyond those associated with each individual treatment modality. Although psychosocial treatments show promise for the treatment of negative symptoms, there are many unanswered questions about how best to intervene. We conclude with a general discussion of these unanswered questions, future directions and methodological considerations, and suggestions for the further development of negative symptom interventions
Low-Density Code-Domain NOMA: Better Be Regular
A closed-form analytical expression is derived for the limiting empirical
squared singular value density of a spreading (signature) matrix corresponding
to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA)
with regular random user-resource allocation. The derivation relies on
associating the spreading matrix with the adjacency matrix of a large
semiregular bipartite graph. For a simple repetition-based sparse spreading
scheme, the result directly follows from a rigorous analysis of spectral
measures of infinite graphs. Turning to random (sparse) binary spreading, we
harness the cavity method from statistical physics, and show that the limiting
spectral density coincides in both cases. Next, we use this density to compute
the normalized input-output mutual information of the underlying vector channel
in the large-system limit. The latter may be interpreted as the achievable
total throughput per dimension with optimum processing in a corresponding
multiple-access channel setting or, alternatively, in a fully-symmetric
broadcast channel setting with full decoding capabilities at each receiver.
Surprisingly, the total throughput of regular LDCD-NOMA is found to be not only
superior to that achieved with irregular user-resource allocation, but also to
the total throughput of dense randomly-spread NOMA, for which optimum
processing is computationally intractable. In contrast, the superior
performance of regular LDCD-NOMA can be potentially achieved with a feasible
message-passing algorithm. This observation may advocate employing regular,
rather than irregular, LDCD-NOMA in 5G cellular physical layer design.Comment: Accepted for publication in the IEEE International Symposium on
Information Theory (ISIT), June 201
Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
We study the asymmetric zero-range process (ZRP) with L sites and open
boundaries, conditioned to carry an atypical current. Using a generalized Doob
h-transform we compute explicitly the transition rates of an effective process
for which the conditioned dynamics are typical. This effective process is a
zero-range process with renormalized hopping rates, which are space dependent
even when the original rates are constant. This leads to non-trivial density
profiles in the steady state of the conditioned dynamics, and, under generic
conditions on the jump rates of the unconditioned ZRP, to an intriguing
supercritical bulk region where condensates can grow. These results provide a
microscopic perspective on macroscopic fluctuation theory (MFT) for the weakly
asymmetric case: It turns out that the predictions of MFT remain valid in the
non-rigorous limit of finite asymmetry. In addition, the microscopic results
yield the correct scaling factor for the asymmetry that MFT cannot predict.Comment: 26 pages, 4 figure
Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium
The equation which describes a particle diffusing in a logarithmic potential
arises in diverse physical problems such as momentum diffusion of atoms in
optical traps, condensation processes, and denaturation of DNA molecules. A
detailed study of the approach of such systems to equilibrium via a scaling
analysis is carried out, revealing three surprising features: (i) the solution
is given by two distinct scaling forms, corresponding to a diffusive (x ~
\sqrt{t}) and a subdiffusive (x >> \sqrt{t}) length scales, respectively; (ii)
the scaling exponents and scaling functions corresponding to both regimes are
selected by the initial condition; and (iii) this dependence on the initial
condition manifests a "phase transition" from a regime in which the scaling
solution depends on the initial condition to a regime in which it is
independent of it. The selection mechanism which is found has many similarities
to the marginal stability mechanism which has been widely studied in the
context of fronts propagating into unstable states. The general scaling forms
are presented and their practical and theoretical applications are discussed.Comment: 42 page
A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I - Basic Formulation and a Conjecture
Einstein's equations are known to lead to the formation of black holes and
spacetime singularities. This appears to be a manifestation of the mathematical
phenomenon of finite-time blowup: a formation of singularities from regular
initial data. We present a simple hyperbolic system of two semi-linear
equations inspired by the Einstein equations. We explore a class of solutions
to this system which are analogous to static black-hole models. These solutions
exhibit a black-hole structure with a finite-time blowup on a characteristic
line mimicking the null inner horizon of spinning or charged black holes. We
conjecture that this behavior - namely black-hole formation with blow-up on a
characteristic line - is a generic feature of our semi-linear system. Our
simple system may provide insight into the formation of null singularities
inside spinning or charged black holes in the full system of Einstein
equations.Comment: 39 pages, 3 figures, extended versio
Are physical objects necessarily burnt up by the blue sheet inside a black hole?
The electromagnetic radiation that falls into a Reissner-Nordstrom black hole
develops a ``blue sheet'' of infinite energy density at the Cauchy horizon. We
consider classical electromagnetic fields (that were produced during the
collapse and then backscattered into the black hole), and investigate the
blue-sheet effects of these fields on infalling objects within a simplified
model. These effects are found to be finite and even negligible for typical
parameters.Comment: 13 pages, ordinary LaTex. Accepted for Physical Review Letters
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