3,680 research outputs found
Fractional unit root tests allowing for a structural change in trend under both the null and alternative hypotheses
This paper considers testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. We extend the Lagrange Multiplier (LM) tests of Robinson (1994) and Tanaka (1999), which are locally best invariant and uniformly most powerful, to allow for a slope change in trend with or without a concurrent level shift under both the null and alternative hypotheses. We show that the limit distribution of the proposed LM tests is standard normal. Finite sample simulation experiments show that the tests have good size and power. As an empirical analysis, we apply the tests to the Consumer Price Indices of the G7 countries
Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes
Birth-death processes take place ubiquitously throughout the universe. In
general, birth and death rates depend on the system size (corresponding to the
number of products or customers undergoing the birth-death process) and thus
vary every time birth or death occurs, which makes fluctuations in the rates
inevitable. The differential-difference equation governing the time evolution
of such a birth-death process is well established, but it resists solving for a
non-asymptotic solution. In this work, we present the analytic solution of the
differential-difference equation for birth-death processes without
approximation. The time-dependent solution we obtain leads to an analytical
expression for counting statistics of products (or customers). We further
examine the relationship between the system size fluctuations and the birth and
death rates, and find that statistical properties (variance subtracted by mean)
of the system size are determined by the mean death rate as well as the
covariance of the system size and the net growth rate (i.e., the birth rate
minus the death rate). This work suggests a promising new direction for
quantitative investigations into birth-death processes
Homotopy Structure of 5d Vacua
It is shown that flat zero-energy solutions (vacua) of the 5d Kaluza-Klein
theory admit a non-trivial homotopy structure generated by certain Kaluza-Klein
excitations. These vacua consist of an infinite set of homotopically different
spacetimes denoted by , among which
and are especially identified as and
, the ground states of the 5d Kaluza-Klein theory and the 5d general
relativity, respectively (where represents the -dimensional Minkowski
space).Comment: 8 page
Exploring Practitioner Perspectives On Training Data Attribution Explanations
Explainable AI (XAI) aims to provide insight into opaque model reasoning to
humans and as such is an interdisciplinary field by nature. In this paper, we
interviewed 10 practitioners to understand the possible usability of training
data attribution (TDA) explanations and to explore the design space of such an
approach. We confirmed that training data quality is often the most important
factor for high model performance in practice and model developers mainly rely
on their own experience to curate data. End-users expect explanations to
enhance their interaction with the model and do not necessarily prioritise but
are open to training data as a means of explanation. Within our participants,
we found that TDA explanations are not well-known and therefore not used. We
urge the community to focus on the utility of TDA techniques from the
human-machine collaboration perspective and broaden the TDA evaluation to
reflect common use cases in practice.Comment: Accepted to NeurIPS XAI in Action workshop 202
Impact angle control guidance synthesis for evasive maneuver against intercept missile
This paper proposes a synthesis of new guidance law to generate an evasive maneuver against enemy’s missile interception while considering its impact angle, acceleration, and field-of-view constraints. The first component of the synthesis is a new function of repulsive Artificial Potential Field to generate the evasive maneuver as a real-time dynamic obstacle avoidance. The terminal impact angle and terminal acceleration constraints compliance are based on Time-to-Go Polynomial Guidance as the second component. The last component is the Logarithmic Barrier Function to satisfy the field-of-view limitation constraint by compensating the excessive total acceleration command. These three components are synthesized into a new guidance law, which involves three design parameter gains. Parameter study and numerical simulations are delivered to demonstrate the performance of the proposed repulsive function and guidance law. Finally, the guidance law simulations effectively achieve the zero terminal miss distance, while satisfying an evasive maneuver against intercept missile, considering impact angle, acceleration, and field-of-view limitation constraints simultaneously
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