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In this paper we examine the use of low-rank approximations for the handling of radiation boundary conditions in a transient heat equation given a cavity radiation setting. The finite element discretization that arises from cavity radiation is well known to be dense, which poses difficulties for efficiency and scalability of solvers. Here we consider a special treatment of the cavity radiation discretization using a block low-rank approximation combined with hierarchical matrices. We provide an overview of the methodology and discusses techniques that can be used to improve efficiency within the framework of hierarchical matrices, including the usage of the approximate cross approximation (ACA) method. We provide a number of numerical results that demonstrate the accuracy and efficiency of the approach in practical problems, and demonstrate significant speedup and memory reduction compared to the more conventional "dense matrix" approach.

Code verification plays an important role in establishing the credibility of computational simulations by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, the numerical solution to integral equations incurs multiple interacting sources of numerical error, as well as other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the combined-field integral equation. We demonstrate the effectiveness of these approaches for cases with and without coding errors.

We propose a new concept, oblivious quantum computation, which requires performing oblivious transfer with respect to the computation outcome of the quantum computation, where the secrecy of the input qubits and the program to identify the quantum gates are required. Exploiting quantum teleportation, we propose a two-server protocol for this task, which realizes an exponential improvement for the communication complexity over the simple application of two-server (quantum) oblivious transfer to the sending of the computation result. Also, we discuss delegated multiparty quantum computation, in which, several users ask multiparty quantum computation to server(s) only using classical communications. We propose a two-server protocol for the latter task as well.

In a recent paper published in the Journal of Language Evolution, Kauhanen, Einhaus & Walkden (//doi.org/10.1093/jole/lzad005, KEW) challenge the results presented in one of my papers (Koplenig, Royal Society Open Science, 6, 181274 (2019), //doi.org/10.1098/rsos.181274), in which I tried to show through a series of statistical analyses that large numbers of L2 (second language) speakers do not seem to affect the (grammatical or statistical) complexity of a language. To this end, I focus on the way in which the Ethnologue assesses language status: a language is characterised as vehicular if, in addition to being used by L1 (first language) speakers, it should also have a significant number of L2 users. KEW criticise both the use of vehicularity as a (binary) indicator of whether a language has a significant number of L2 users and the idea of imputing a zero proportion of L2 speakers to non-vehicular languages whenever a direct estimate of that proportion is unavailable. While I recognise the importance of post-publication commentary on published research, I show in this rejoinder that both points of criticism are explicitly mentioned and analysed in my paper. In addition, I also comment on other points raised by KEW and demonstrate that both alternative analyses offered by KEW do not stand up to closer scrutiny.

A contiguous area cartogram is a geographic map in which the area of each region is proportional to numerical data (e.g., population size) while keeping neighboring regions connected. In this study, we investigated whether value-to-area legends (square symbols next to the values represented by the squares' areas) and grid lines aid map readers in making better area judgments. We conducted an experiment to determine the accuracy, speed, and confidence with which readers infer numerical data values for the mapped regions. We found that, when only informed about the total numerical value represented by the whole cartogram without any legend, the distribution of estimates for individual regions was centered near the true value with substantial spread. Legends with grid lines significantly reduced the spread but led to a tendency to underestimate the values. Comparing differences between regions or between cartograms revealed that legends and grid lines slowed the estimation without improving accuracy. However, participants were more likely to complete the tasks when legends and grid lines were present, particularly when the area units represented by these features could be interactively selected. We recommend considering the cartogram's use case and purpose before deciding whether to include grid lines or an interactive legend.

This paper considers the phenomenon where a single probe to a target generates multiple, sometimes numerous, packets in response -- which we term "blowback". Understanding blowback is important because attackers can leverage it to launch amplified denial of service attacks by redirecting blowback towards a victim. Blowback also has serious implications for Internet researchers since their experimental setups must cope with bursts of blowback traffic. We find that tens of thousands, and in some protocols, hundreds of thousands, of hosts generate blowback, with orders of magnitude amplification on average. In fact, some prolific blowback generators produce millions of response packets in the aftermath of a single probe. We also find that blowback generators are fairly stable over periods of weeks, so once identified, many of these hosts can be exploited by attackers for a long time.

We consider $t$-Lee-error-correcting codes of length $n$ over the residue ring $\mathbb{Z}_m := \mathbb{Z}/m\mathbb{Z}$ and determine upper and lower bounds on the number of $t$-Lee-error-correcting codes. We use two different methods, namely estimating isolated nodes on bipartite graphs and the graph container method. The former gives density results for codes of fixed size and the latter for any size. This confirms some recent density results for linear Lee metric codes and provides new density results for nonlinear codes. To apply a variant of the graph container algorithm we also investigate some geometrical properties of the balls in the Lee metric.

We consider a standard two-source model for uniform common randomness (UCR) generation, in which Alice and Bob observe independent and identically distributed (i.i.d.) samples of a correlated finite source and where Alice is allowed to send information to Bob over an arbitrary single-user channel. We study the \(\boldsymbol{\epsilon}\)-UCR capacity for the proposed model, defined as the maximum common randomness rate one can achieve such that the probability that Alice and Bob do not agree on a common uniform or nearly uniform random variable does not exceed \(\boldsymbol{\epsilon}.\) We establish a lower and an upper bound on the \(\boldsymbol{\epsilon}\)-UCR capacity using the bounds on the \(\boldsymbol{\epsilon}\)-transmission capacity proved by Verd\'u and Han for arbitrary point-to-point channels.

We study an envy-free pricing problem, in which each buyer wishes to buy a shortest path connecting her individual pair of vertices in a network owned by a single vendor. The vendor sets the prices of individual edges with the aim of maximizing the total revenue generated by all buyers. Each customer buys a path as long as its cost does not exceed her individual budget. In this case, the revenue generated by her equals the sum of prices of edges along this path. We consider the unlimited supply setting, where each edge can be sold to arbitrarily many customers. The problem is to find a price assignment which maximizes vendor's revenue. A special case in which the network is a tree is known under the name of the tollbooth problem. Gamzu and Segev proposed a $\mathcal{O} \left( \frac{\log m}{\log \log m} \right)$-approximation algorithm for revenue maximization in that setting. Note that paths in a tree network are unique, and hence the tollbooth problem falls under the category of single-minded bidders, i.e., each buyer is interested in a single fixed set of goods. In this work we step out of the single-minded setting and consider more general networks that may contain cycles. We obtain an algorithm for pricing cactus shaped networks, namely networks in which each edge can belong to at most one simple cycle. Our result is a polynomial time $\mathcal{0} \left( \frac{\log m}{\log \log m}\right)$-approximation algorithm for revenue maximization in tollbooth pricing on a cactus graph. It builds upon the framework of Gamzu and Segev, but requires substantially extending its main ideas: the recursive decomposition of the graph, the dynamic programming for rooted instances and rounding the prices.

Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function $f(x,y)$, where $x$ is given to Alice and $y$ is given to Bob, and only one message from Alice to Bob is allowed. A fundamental question in quantum information is the relationship between one-way quantum and classical communication complexities, i.e., how much shorter the message can be if Alice is sending a quantum state instead of bit strings? We make some progress towards this question with the following results. Let $f: \mathcal{X} \times \mathcal{Y} \rightarrow \mathcal{Z} \cup \{\bot\}$ be a partial function and $\mu$ be a distribution with support contained in $f^{-1}(\mathcal{Z})$. Denote $d=|\mathcal{Z}|$. Let $\mathsf{R}^{1,\mu}_\epsilon(f)$ be the classical one-way communication complexity of $f$; $\mathsf{Q}^{1,\mu}_\epsilon(f)$ be the quantum one-way communication complexity of $f$ and $\mathsf{Q}^{1,\mu, *}_\epsilon(f)$ be the entanglement-assisted quantum one-way communication complexity of $f$, each with distributional error (average error over $\mu$) at most $\epsilon$. We show: 1) If $\mu$ is a product distribution, $\eta > 0$ and $0 \leq \epsilon \leq 1-1/d$, then, $$\mathsf{R}^{1,\mu}_{2\epsilon -d\epsilon^2/(d-1)+ \eta}(f) \leq 2\mathsf{Q}^{1,\mu, *}_{\epsilon}(f) + O(\log\log (1/\eta))\enspace.$$ 2)If $\mu$ is a non-product distribution and $\mathcal{Z}=\{ 0,1\}$, then $\forall \epsilon, \eta > 0$ such that $\epsilon/\eta + \eta < 0.5$, $$\mathsf{R}^{1,\mu}_{3\eta}(f) = O(\mathsf{Q}^{1,\mu}_{{\epsilon}}(f) \cdot \mathsf{CS}(f)/\eta^3)\enspace,$$ where \[\mathsf{CS}(f) = \max_{y} \min_{z\in\{0,1\}} \vert \{x~|~f(x,y)=z\} \vert \enspace.\]