A Massively Parallel 2D Rectangle Placement Method

Layout design is a frequently occurring process that oftencombines human and computer reasoning. Because of the combinatorialnature of the problem, solving even a small size input involves searchinga prohibitively large state space. An algorithm PEMS (Pseudo-exhaustiveEdge Minimizing Search) is proposed for approximating a 2D rectanglepacking variant of the problem. The proposed method is inspiredby MERA (Minimum Enclosing of Rectangle Area) [1] and MEGA(Minimum Enclosing Under Gravitational Attraction) [2], yet produceshigher quality solutions, in terms of final space utilization. To addressthe performance cost, a CUDA based acceleration algorithm is developedwith significant speedup

The HI Mass Function and Velocity Width Function of Void Galaxies in the Arecibo Legacy Fast ALFA Survey

We measure the HI mass function (HIMF) and velocity width function (WF) across environments over a range of masses $7.2<\log(M_{HI}/M_{\odot})<10.8$, and profile widths $1.3\log(km/s)<\log(W)<2.9\log(km/s)$, using a catalog of ~7,300 HI-selected galaxies from the ALFALFA Survey, located in the region of sky where ALFALFA and SDSS (Data Release 7) North overlap. We divide our galaxy sample into those that reside in large-scale voids (void galaxies) and those that live in denser regions (wall galaxies). We find the void HIMF to be well fit by a Schechter function with normalization $\Phi^*=(1.37\pm0.1)\times10^{-2} h^3Mpc^{-3}$, characteristic mass $\log(M^*/M_{\odot})+2\log h_{70}=9.86\pm0.02$, and low-mass-end slope $\alpha=-1.29\pm0.02$. Similarly, for wall galaxies, we find best-fitting parameters $\Phi^*=(1.82\pm0.03)\times10^{-2} h^3Mpc^{-3}$, $\log(M^*/M_{\odot})+2\log h_{70}=10.00\pm0.01$, and $\alpha=-1.35\pm0.01$. We conclude that void galaxies typically have slightly lower HI masses than their non-void counterparts, which is in agreement with the dark matter halo mass function shift in voids assuming a simple relationship between DM mass and HI mass. We also find that the low-mass slope of the void HIMF is similar to that of the wall HIMF suggesting that there is either no excess of low-mass galaxies in voids or there is an abundance of intermediate HI mass galaxies. We fit a modified Schechter function to the ALFALFA void WF and determine its best-fitting parameters to be $\Phi^*=0.21\pm0.1 h^3Mpc^{-3}$, $\log(W^*)=2.13\pm0.3$, $\alpha=0.52\pm0.5$ and high-width slope $\beta=1.3\pm0.4$. For wall galaxies, the WF parameters are: $\Phi^*=0.022\pm0.009 h^3Mpc^{-3}$, $\log(W^*)=2.62\pm0.5$, $\alpha=-0.64\pm0.2$ and $\beta=3.58\pm1.5$. Because of large uncertainties on the void and wall width functions, we cannot conclude whether the WF is dependent on the environment.Comment: Accepted for publication at MNRAS, 14 pages, 12 figure

SHARP: Sparsity and Hidden Activation RePlay for Neuro-Inspired Continual Learning

Deep neural networks (DNNs) struggle to learn in dynamic environments since they rely on fixed datasets or stationary environments. Continual learning (CL) aims to address this limitation and enable DNNs to accumulate knowledge incrementally, similar to human learning. Inspired by how our brain consolidates memories, a powerful strategy in CL is replay, which involves training the DNN on a mixture of new and all seen classes. However, existing replay methods overlook two crucial aspects of biological replay: 1) the brain replays processed neural patterns instead of raw input, and 2) it prioritizes the replay of recently learned information rather than revisiting all past experiences. To address these differences, we propose SHARP, an efficient neuro-inspired CL method that leverages sparse dynamic connectivity and activation replay. Unlike other activation replay methods, which assume layers not subjected to replay have been pretrained and fixed, SHARP can continually update all layers. Also, SHARP is unique in that it only needs to replay few recently seen classes instead of all past classes. Our experiments on five datasets demonstrate that SHARP outperforms state-of-the-art replay methods in class incremental learning. Furthermore, we showcase SHARP's flexibility in a novel CL scenario where the boundaries between learning episodes are blurry. The SHARP code is available at \url{https://github.com/BurakGurbuz97/SHARP-Continual-Learning}

Time- and Communication-Efficient Overlay Network Construction via Gossip

We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it knows. The network is assumed to be reconfigurable, i.e., a node can add new connections (edges) to other nodes whose identifier it knows or drop existing connections. Each node initially has only knowledge of its own identifier and the identifiers of its neighbors. The overlay construction problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a bounded-degree expander graph as efficiently as possible. The overlay construction problem is relevant to building real-world peer-to-peer network topologies that have desirable properties such as low diameter, high conductance, robustness to adversarial deletions, etc. Our main result is that we show that starting from any arbitrary (connected) graph $G$ on $n$ nodes and $m$ edges, we can construct an overlay network that is a constant-degree expander in polylog $n$ rounds using only $\tilde{O}(n)$ messages. Our time and message bounds are both essentially optimal (up to polylogarithmic factors). Our distributed overlay construction protocol is very lightweight as it uses gossip (each node communicates with only one neighbor in each round) and also scalable as it uses only $\tilde{O}(n)$ messages, which is sublinear in $m$ (even when $m$ is moderately dense). To the best of our knowledge, this is the first result that achieves overlay network construction in polylog $n$ rounds and $o(m)$ messages. Our protocol uses graph sketches in a novel way to construct an expander overlay that is both time and communication efficient. A consequence of our overlay construction protocol is that distributed computation can be performed very efficiently in this model.Comment: Slightly shortened abstrac

Estimating Atrazine Leaching in the Midwest

Data from seven Management Systems Evaluation Areas (MSEM) were used to test the sensitivity of a leaching model, PRZM-2, to a variety of hydrologic settings common in the Midwest. Atrazine leaching was simulated because the use of atrazine was prevalent in the MSEA studies and it frequently occurs in the region\u27s groundwater. Results of long-term simulations using regional and generalized input parameters produced ranks of leaching potential similar to those based on measurements. Short-term simulations used site-specific soil and chemical coefficients

Counting Rotational Sets for Laminations of the Unit Disk from First Principles

By studying laminations of the unit disk, we can gain insight into the structure of Julia sets of polynomials and their dynamics in the complex plane. The polynomials of a given degree, $d$, have a parameter space. The hyperbolic components of such parameter spaces are in correspondence to rotational polygons, or classes of "rotational sets", which we study in this paper. By studying the count of such rotational sets, and therefore the underlying structure behind these rotational sets and polygons, we can gain insight into the interrelationship among hyperbolic components of the parameter space of these polynomials. These rotational sets are created by uniting rotational orbits, as we define in this paper. The number of such sets for a given degree $d$, rotation number $\frac pq$, and cardinality $k$ can be determined by analyzing the potential placements of pre-images of zero on the unit circle with respect to the rotational set under the $d$-tupling map. We obtain a closed-form formula for the count. Though this count is already known based upon some sophisticated results, our count is based upon elementary geometric and combinatorial principles, and provides an intuitive explanation.Comment: 12 pages, 5 figure