Tracking an Auto-Regressive Process with Limited Communication per Unit Time

Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.

Universally Optimal One-sided Circular Neighbour-balanced Designs with k = 5

In many experiments, especially in agriculture and horticulture to some extent, the response from a plot in a block is affected by treatments on forward (backward) neighbour plots in the same block. Under such circumstances, one-sided circular neighbour-balanced design (one-sided CNBD) has wide applications. However, in concern with the universal optimality, there are very limited number of known series of one-sided CNBD’s. The purpose of this article is to present a new series of universally optimal one-sided CNBD with block size 5 where if a treatment appears repeatedly in a block, all of them are in a series of adjacent plots in the block.

Erratum: Energy Minimization, Periodic Sets, and Spherical Designs

In [ 3] we considered energy minimization of pair potentials among periodic sets of a fixed-point density. For a large class of potentials we presented sufficient conditions for a point lattice to give a local optimum among periodic sets. We hereby, in particular, derived a local version of Cohn and Kumar’s conjecture [ 1, Conjecture 9.4] by which the hexagonal lattice $\textsf{A}_2$, the root lattice $\textsf{E}_8$, and the Leech lattice are globally universally optimal. Latter conjecture has recently been proved for $\textsf{E}_8$ and the Leech lattice by Cohn et al. [ 2].

Attention Management

Attention costs can cause some information to be ignored and decisions to be imperfect. Can we improve the material welfare of a rationally inattentive agent by restricting his information in the first place? In our model, a well-intentioned principal provides information to an agent for whom information is costly to process, but the principal does not internalize this cost. We show that full information is universally optimal if and only if the environment comprises one issue. With multiple issues, attention management becomes optimal: the principal restricts some information to induce the agent to pay attention to other aspects. (JEL D82, D83, D91)

Optimization of the Navigated TMS Mapping Algorithm for Accurate Estimation of Cortical Muscle Representation Characteristics

Navigated transcranial magnetic stimulation (nTMS) mapping of cortical muscle representations allows noninvasive assessment of the state of a healthy or diseased motor system, and monitoring changes over time. These applications are hampered by the heterogeneity of existing mapping algorithms and the lack of detailed information about their accuracy. We aimed to find an optimal motor evoked potential (MEP) sampling scheme in the grid-based mapping algorithm in terms of the accuracy of muscle representation parameters. The abductor pollicis brevis (APB) muscles of eight healthy subjects were mapped three times on consecutive days using a seven-by-seven grid with ten stimuli per cell. The effect of the MEP variability on the parameter accuracy was assessed using bootstrapping. The accuracy of representation parameters increased with the number of stimuli without saturation up to at least ten stimuli per cell. The detailed sampling showed that the between-session representation area changes in the absence of interventions were significantly larger than the within-session fluctuations and thus could not be explained solely by the trial-to-trial variability of MEPs. The results demonstrate that the number of stimuli has no universally optimal value and must be chosen by balancing the accuracy requirements with the mapping time constraints in a given problem.