7,939 research outputs found
Crystallization of random trigonometric polynomials
We give a precise measure of the rate at which repeated differentiation of a
random trigonometric polynomial causes the roots of the function to approach
equal spacing. This can be viewed as a toy model of crystallization in one
dimension. In particular we determine the asymptotics of the distribution of
the roots around the crystalline configuration and find that the distribution
is not Gaussian.Comment: 10 pages, 3 figure
Reviews
Review of The Industrial Relations Amending Legislation of 1976, Industrial Conflict: A Study of Three New Zealand Industries, A Seventh Man, Economists at Bay - Why the Experts Will Never Solve Your Problem
Statistical theory of the continuous double auction
Most modern financial markets use a continuous double auction mechanism to
store and match orders and facilitate trading. In this paper we develop a
microscopic dynamical statistical model for the continuous double auction under
the assumption of IID random order flow, and analyze it using simulation,
dimensional analysis, and theoretical tools based on mean field approximations.
The model makes testable predictions for basic properties of markets, such as
price volatility, the depth of stored supply and demand vs. price, the bid-ask
spread, the price impact function, and the time and probability of filling
orders. These predictions are based on properties of order flow and the limit
order book, such as share volume of market and limit orders, cancellations,
typical order size, and tick size. Because these quantities can all be measured
directly there are no free parameters. We show that the order size, which can
be cast as a nondimensional granularity parameter, is in most cases a more
significant determinant of market behavior than tick size. We also provide an
explanation for the observed highly concave nature of the price impact
function. On a broader level, this work suggests how stochastic models based on
zero-intelligence agents may be useful to probe the structure of market
institutions. Like the model of perfect rationality, a stochastic-zero
intelligence model can be used to make strong predictions based on a compact
set of assumptions, even if these assumptions are not fully believable.Comment: 36 pages, 40 figures, RevTex4, submitted to Quantitative Financ
Random polynomials, random matrices, and -functions
We show that the Circular Orthogonal Ensemble of random matrices arises
naturally from a family of random polynomials. This sheds light on the
appearance of random matrix statistics in the zeros of the Riemann
zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit
Market impact and trading profile of large trading orders in stock markets
We empirically study the market impact of trading orders. We are specifically
interested in large trading orders that are executed incrementally, which we
call hidden orders. These are reconstructed based on information about market
member codes using data from the Spanish Stock Market and the London Stock
Exchange. We find that market impact is strongly concave, approximately
increasing as the square root of order size. Furthermore, as a given order is
executed, the impact grows in time according to a power-law; after the order is
finished, it reverts to a level of about 0.5-0.7 of its value at its peak. We
observe that hidden orders are executed at a rate that more or less matches
trading in the overall market, except for small deviations at the beginning and
end of the order.Comment: 9 pages, 7 figure
A Bit-String Model for Biological Aging
We present a simple model for biological aging. We studied it through
computer simulations and we have found this model to reflect some features of
real populations.Comment: LaTeX file, 4 PS figures include
Chirped pulse Raman amplification in plasma: high gain measurements
High power short pulse lasers are usually based on chirped pulse amplification (CPA), where a frequency chirped and temporarily stretched ``seed'' pulse is amplified by a broad-bandwidth solid state medium, which is usually pumped by a monochromatic ``pump'' laser. Here, we demonstrate the feasibility of using chirped pulse Raman amplification (CPRA) as a means of amplifying short pulses in plasma. In this scheme, a short seed pulse is amplified by a stretched and chirped pump pulse through Raman backscattering in a plasma channel. Unlike conventional CPA, each spectral component of the seed is amplified at different longitudinal positions determined by the resonance of the seed, pump and plasma wave, which excites a density echelon that acts as a "chirped'" mirror and simultaneously backscatters and compresses the pump. Experimental evidence shows that it has potential as an ultra-broad bandwidth linear amplifier which dispenses with the need for large compressor gratings
Returning children home from care: What can be learned from local authority data?
International Human Rights and child rights conventions as well as U.K. wide legislation and guidance require that children in care should be returned home to one or both parents wherever possible. Reunification with parents is the most common route out of care, but rates of reāentry are often higher than for other exit routes. This study used 8 years of administrative data (on 2,208 care entrants), collected by one large English local authority, to examine how many children were returned home and to explore factors associated with stable reunification (not reāentering care for at least 2 years). Oneāthird of children (36%) had been reunified, with adolescent entrants being the most likely age group to return home. Three quarters (75%) of reunified children had a stable reunification. In a fully adjusted regression model, age at entry, being on a care order prior to return home, staying longer in care, being of minority ethnicity, and having fewer placements in care were all significant in predicting chances of stable reunification. The results underline the importance of properly resourcing reunification services. The methods demonstrate the value to local authorities of analysing their own data longitudinally to understand the care pathways for children they look after
Controlling Fast Chaos in Delay Dynamical Systems
We introduce a novel approach for controlling fast chaos in time-delay
dynamical systems and use it to control a chaotic photonic device with a
characteristic time scale of ~12 ns. Our approach is a prescription for how to
implement existing chaos control algorithms in a way that exploits the system's
inherent time-delay and allows control even in the presence of substantial
control-loop latency (the finite time it takes signals to propagate through the
components in the controller). This research paves the way for applications
exploiting fast control of chaos, such as chaos-based communication schemes and
stabilizing the behavior of ultrafast lasers.Comment: 4 pages, 4 figures, to be published in Physical Review Letter
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