The walking robot project

A walking robot was designed, analyzed, and tested as an intelligent, mobile, and a terrain adaptive system. The robot's design was an application of existing technologies. The design of the six legs modified and combines well understood mechanisms and was optimized for performance, flexibility, and simplicity. The body design incorporated two tripods for walking stability and ease of turning. The electrical hardware design used modularity and distributed processing to drive the motors. The software design used feedback to coordinate the system and simple keystrokes to give commands. The walking machine can be easily adapted to hostile environments such as high radiation zones and alien terrain. The primary goal of the leg design was to create a leg capable of supporting a robot's body and electrical hardware while walking or performing desired tasks, namely those required for planetary exploration. The leg designers intent was to study the maximum amount of flexibility and maneuverability achievable by the simplest and lightest leg design. The main constraints for the leg design were leg kinematics, ease of assembly, degrees of freedom, number of motors, overall size, and weight

Multiscale models of colloidal dispersion of particles in nematic liquid crystals

We use homogenization theory to develop a multiscale model of colloidal dispersion of particles in nematic liquid crystals under weak-anchoring conditions. We validate the model by comparing it with simulations by using the Landau–de Gennes free energy and show that the agreement is excellent. We then use the multiscale model to study the effect that particle anisotropy has on the liquid crystal: spherically symmetric particles always reduce the effective elastic constant. Asymmetric particles introduce an effective alignment field that can increase the Fredericks threshold and decrease the switch-off time

Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs

Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we present a possibly simpler proof of the result in [CLNV15] and strengthen the result to show that it is PSPACE-hard to determine the minimum number of pebbles to an additive $n^{1/3-\epsilon}$ term for all $\epsilon > 0$, which improves upon the currently known additive constant hardness of approximation [CLNV15] in the standard pebble game. We also introduce a family of explicit, constant indegree graphs with $n$ nodes where there exists a graph in the family such that using constant $k$ pebbles requires $\Omega(n^k)$ moves to pebble in both the standard and black-white pebble games. This independently answers an open question summarized in [Nor15] of whether a family of DAGs exists that meets the upper bound of $O(n^k)$ moves using constant $k$ pebbles with a different construction than that presented in [AdRNV17].Comment: Preliminary version in WADS 201

Classification by means of B-spline potential functions with applications to remote sensing

A method is presented for using B-splines as potential functions in the estimation of likelihood functions (probability density functions conditioned on pattern classes), or the resulting discriminant functions. The consistency of this technique is discussed. Experimental results of using the likelihood functions in the classification of remotely sensed data are given

A method of enciphering quantum states

In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the Intercept/Resend attack), a probability that Alice and Bob do not notice Eve's action is equal to (3/4)^m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack with using entanglement. This remains to be solved in the future.Comment: 21 pages, Latex2e, 10 epsf figures. v2: 22 pages, added two references, several clarifying sentences are added in Sec. 5, typos corrected, a new proof is provided in Appendix A and it is shorter than the old one. v3: 23 pages, one section is adde

The Initial Value Problem For Maximally Non-Local Actions

We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at most discretely enlarged, and may even be restricted, with respect to that of a local theory. We show that the solutions are those of a local theory whose (spacetime constant) parameters vary with the initial value data according to algebraic equations. The various roots of these algebraic equations can be plausibly interpreted in quantum mechanics as different components of a multi-component wave function. It is also possible that the consistency of these algebraic equations imposes constraints upon the initial value data which appear miraculous from the context of a local theory.Comment: 8 pages, LaTeX 2 epsilo

Entanglement required in achieving entanglement-assisted channel capacities

Entanglement shared between the two ends of a quantum communication channel has been shown to be a useful resource in increasing both the quantum and classical capacities for these channels. The entanglement-assisted capacities were derived assuming an unlimited amount of shared entanglement per channel use. In this paper, bounds are derived on the minimum amount of entanglement required per use of a channel, in order to asymptotically achieve the capacity. This is achieved by introducing a class of entanglement-assisted quantum codes. Codes for classes of qubit channels are shown to achieve the quantum entanglement-assisted channel capacity when an amount of shared entanglement per channel given by, E = 1 - Q_E, is provided. It is also shown that for very noisy channels, as the capacities become small, the amount of required entanglement converges for the classical and quantum capacities.Comment: 9 pages, 2 figures, RevTex

Estimating the risk of adverse birth outcomes in pregnant women undergoing non-obstetric surgery using routinely collected NHS data: an observational study

Background: Previous research suggests that non-obstetric surgery is carried out in 1 – 2% of all pregnancies. However, there is limited evidence quantifying the associated risks. Furthermore, of the evidence available, none relates directly to outcomes in the UK, and there are no current NHS guidelines regarding non-obstetric surgery in pregnant women. Objectives: To estimate the risk of adverse birth outcomes of pregnancies in which non-obstetric surgery was or was not carried out. To further analyse common procedure groups. Data Source: Hospital Episode Statistics (HES) maternity data collected between 2002 – 3 and 2011 – 12. Main outcomes: Spontaneous abortion, preterm delivery, maternal death, caesarean delivery, long inpatient stay, stillbirth and low birthweight. Methods: We utilised HES, an administrative database that includes records of all patient admissions and day cases in all English NHS hospitals. We analysed HES maternity data collected between 2002 – 3 and 2011 – 12, and identified pregnancies in which non-obstetric surgery was carried out. We used logistic regression models to determine the adjusted relative risk and attributable risk of non-obstetric surgical procedures for adverse birth outcomes and the number needed to harm. Results: We identified 6,486,280 pregnancies, in 47,628 of which non-obstetric surgery was carried out. In comparison with pregnancies in which surgery was not carried out, we found that non-obstetric surgery was associated with a higher risk of adverse birth outcomes, although the attributable risk was generally low. We estimated that for every 287 pregnancies in which a surgical operation was carried out there was one additional stillbirth; for every 31 operations there was one additional preterm delivery; for every 25 operations there was one additional caesarean section; for every 50 operations there was one additional long inpatient stay; and for every 39 operations there was one additional low-birthweight baby. Limitations: We have no means of disentangling the effect of the surgery from the effect of the underlying condition itself. Many spontaneous abortions will not be associated with a hospital admission and, therefore, will not be included in our analysis. A spontaneous abortion may be more likely to be reported if it occurs during the same hospital admission as the procedure, and this could account for the associated increased risk with surgery during pregnancy. There are missing values of key data items to determine parity, gestational age, birthweight and stillbirth. Conclusions: This is the first study to report the risk of adverse birth outcomes following non-obstetric surgery during pregnancy across NHS hospitals in England. We have no means of disentangling the effect of the surgery from the effect of the underlying condition itself. Our observational study can never attribute a causal relationship between surgery and adverse birth outcomes, and we were unable to determine the risk of not undergoing surgery where surgery was clinically indicated. We have some reservations over associations of risk factors with spontaneous abortion because of potential ascertainment bias. However, we believe that our findings and, in particular, the numbers needed to harm improve on previous research, utilise a more recent and larger data set based on UK practices, and are useful reference points for any discussion of risk with prospective patients. The risk of adverse birth outcomes in pregnant women undergoing non-obstetric surgery is relatively low, confirming that surgical procedures during pregnancy are generally safe. Future work: Further evaluation of the association of non-obstetric surgery and spontaneous abortion. Evaluation of the impact of non-obstetric surgery on the newborn (e.g. neonatal intensive care unit admission, prolonged length of neonatal stay, neonatal death). Funding: The National Institute for Health Research Health Services and Delivery Research programme

Cosmic strings, loops, and linear growth of matter perturbations

We describe the detailed study and results of high-resolution numerical simulations of string-induced structure formation in open universes and those with a non-zero cosmological constant. The effect from small loops generated from the string network has also been investigated. We provide a semi-analytical model which can reproduce these simulation results. A detailed study of cosmic string network properties regarding structure formation is also given, including the correlation time, the topological analysis of the source spectrum, the correlation between long strings and loops, and the evolution of long-string and loop energy densities. For models with $\Gamma=\Omega h=0.1--0.2 and a cold dark matter background, we show that the linear density fluctuation power spectrum induced by cosmic strings has both an amplitude at$8 h^{-1}$Mpc,$\sigma_8$, and an overall shape which are consistent within uncertainties with those currently inferred from galaxy surveys. The cosmic string scenario with hot dark matter requires a strongly scale-dependent bias in order to agree with observations.Comment: 60 pages, 24 figure