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In this paper, we present Mixels, programmable magnetic pixels that can be rapidly fabricated using an electromagnetic printhead mounted on an off-the-shelve 3-axis CNC machine. The ability to program magnetic material pixel-wise with varying magnetic force enables Mixels to create new tangible, tactile, and haptic interfaces. To facilitate the creation of interactive objects with Mixels, we provide a user interface that lets users specify the high-level magnetic behavior and that then computes the underlying magnetic pixel assignments and fabrication instructions to program the magnetic surface. Our custom hardware add-on based on an electromagnetic printhead and hall effect sensor clips onto a standard 3-axis CNC machine and can both write and read magnetic pixel values from magnetic material. Our evaluation shows that our system can reliably program and read magnetic pixels of various strengths, that we can predict the behavior of two interacting magnetic surfaces before programming them, that our electromagnet is strong enough to create pixels that utilize the maximum magnetic strength of the material being programmed, and that this material remains magnetized when removed from the magnetic plotter., Comment: ACM UIST 2022: ACM Symposium on User Interface Software and Technology

Let $C=A(r, r')$ be a closed annulus of radii $r$ and $r'$ ($r < r' \in \mathbb{Q}_{\geq 0}$) over a complete discrete valuation field with algebraically closed residue field of characteristic $p>0$. To an \'etale sheaf of $\mathbb{F}_{\ell}$-modules $\mathcal{F}$ on $C$, ramified at most at a finite set of rigid points of $C$, we associate an Abbes-Saito Swan conductor function $\mathrm{sw}_{\mathrm{AS}}(\mathcal{F}, \cdot): [r, r']\cap \mathbb{Q}_{\geq 0} \to \mathbb{Q}$ which, for the variable $t$, measures the ramification of $\mathcal{F}\lvert C^{[t]}$ - the restriction of $\mathcal{F}$ to the sub-annulus $C^{[t]}$ of $C$ of radius $t$ with $0$-thickness - along the special fiber of the normalized integral model of $C^{[t]}$. We show that this function is continuous, convex and piecewise linear outside the radii of the ramification points of $\mathcal{F}$, with finitely many slopes which are all integers. For two distinct radii $t$ and $t'$ lying between consecutive radii of ramification points of $\mathcal{F}$, we compute the difference of the slopes of $\mathrm{sw}_{\mathrm{AS}}(\mathcal{F}, \cdot)$ at $t$ and $t'$ as the difference of the orders of the characteristic cycles of $\mathcal{F}$ at $t$ and $t'$., Comment: 34 pages. Comments are welcome

This article studies the variation of the Swan conductor of a lisse \'etale sheaf of $\mathbb{F}_{\ell}$-modules $\mathcal{F}$ on the rigid unit disc $D$ over a complete discrete valuation field $K$ with algebraically closed residue field of characteristic $p\neq \ell$. We associate to $\mathcal{F}$ a function ${\rm sw}_{\rm AS}(\mathcal{F}, \cdot): \mathbb{Q}_{\geq 0}\to \mathbb{Q}$, defined with the Abbes-Saito logarithmic ramification filtration, which measures, at each $t\in \mathbb{Q}_{\geq 0}$, the ramification of the restriction of $\mathcal{F}$ to the subdisc of radius $t$ along the special fiber of the normalized integral model. We prove that this function is continuous and piecewise linear, with finitely many slopes which are all integers. We compute the slope at $t\in \mathbb{Q}_{\geq 0}$ in terms of a characteristic cycle associated to $\mathcal{F}$, a (power of a) logarithmic differential form defined by ramification theory., Comment: 60 pages. A sign mistake in the main theorem has been corrected. The proof of the last proposition of the penultimate section has been straightened out

The Johnson-Lindenstrauss Lemma (J-L Lemma) is a cornerstone of dimension reduction techniques. We study it in the one-bit context, namely we consider the unit sphere $ \mathbb S ^{N-1}$, with normalized geodesic metric, and map a finite set $ \mathbf{X} \subset \mathbb{S}^{N-1}$ into the Hamming cube $\mathbb{H}_m = \{0,1\}^m$, with normalized Hamming metric. We find that for $ 0< \delta <1$, and $m>\frac{\ln n}{2\delta^2}$ there is a $\delta$-RIP from $\mathbf{X}$ into $\mathbb{H}_m$. This is surprising as the value of $ m$ is virtually identical to best known bound linear J-L Lemma. In both the linear and one-bit case, the maps are randomly constructed. We show that the probability of $B_m$ being a $\delta$-RIP satisfies a phase transition. It passes from probability of nearly zero to nearly one with a very small change in $m$. Our proof relies on delicate properties of Bernoulli random variables.

We present a new $O(k^2 \binom{n}{k}^2)$ method for generating an orthogonal basis of eigenvectors for the Johnson graph $J(n,k)$. Unlike standard methods for computing a full eigenbasis of sparse symmetric matrices, the algorithm presented here is non-iterative, and produces exact results under an infinite-precision computation model. In addition, our method is highly parallelizable; given access to unlimited parallel processors, the eigenbasis can be constructed in only $O(n)$ time given n and k. We also present an algorithm for computing projections onto the eigenspaces of $J(n,k)$ in parallel time $O(n)$.

In May 1997, USAID's Center for Development Information and Evaluation (CDIE) launched the initiative, "Focus on Girls: An Evaluation of USAID Programs and Policies in Education." The effort included five Impact Evaluations, including this study in Guinea (Guatemala, Malawi, Nepal, and Pakistan were the others). This Impact Evaluation used four methods: (1) document review; (2) analysis of data provided by the Guinean Statistics and Planning Unit; (3) interviews with policy and program actors in Guinean education, from both the Guinean government and donor agencies; and (4) observations, interviews, and focus group discussions with parents, teachers, and local administrators of four primary schools in Lelouma prefecture in Middle Guinea. Findings showed that Guinea has transformed its education system during the 1990s by restructuring the system to emphasize primary schooling, and by expanding school supply. The country's percentage of school-age girls enrolled in primary school rose from 17 percent in 1989 to 37 percent in 1997. Now growing at 16 percent annually, girls' educational participation in Guinea ranks first among African countries for sustained growth. Girls still lag behind boys in persistence and achievement. In 1997, only 57 percent of girls, versus 73 percent of boys reached the final year of primary school, and 33 percent of girls who sat for the seventh-grade entry exam passed, compared with 44 percent of boys. The study's detailed findings included these lessons: (1) basic education reform, coupled with girl-specific policies and programs, is a powerful strategy for improving girls' educational participation; (2) a unified message and activist leadership are critical to increasing girls' education; (3) baseline assessment and analysis are requirements for gender-aware policy and program design; (4) a coherent education policy and investment framework must be applied to girls' education initiatives; (5) change is local; (6) a hybrid of conditionality and "projectized" support was effective in putting girls' education on the agenda; (7) sustained, integrated support is necessary to consolidate the early efforts of Guinea's Ministry of Pre- University Education (MEPU) in girls' education; and (8) simultaneous efforts to improve quality and enhance quantity are needed. (EV)