As he entered Hong Kong Supermarket, Sam Lin scanned text messages from his wife instructing him how many red envelopes to buy. Three dozen, she wrote -- and make them large, to fit checks rather than folded wads of cash. Lin's nephews, nieces and in-laws will not have the thrill of pulling crisp bills out of their red Lunar New Year good luck envelopes when the Year of the Ox begins Friday. Normally, Lin goes to his credit union weeks ahead of the holiday to pre-order new bills -- a total of $900 to $1,000 for the kids and elders in his extended family. But with the possibility that the coronavirus could be lurking on $20 or $100 bills, Lin is one of many Asian Americans forgoing traditional cash to ring in the festivities.

Determinantal point processes (DPPs) are widely popular probabilistic models used in machine learning to capture diversity in random subsets of items. While traditional DPPs are defined by a symmetric kernel matrix, recent work has shown a significant increase in the modeling power and applicability of models defined by nonsymmetric kernels, where the model can capture interactions that go beyond diversity. We study the problem of maximum a posteriori (MAP) inference for determinantal point processes defined by a nonsymmetric positive semidefinite matrix (NDPPs), where the goal is to find the maximum $k\times k$ principal minor of the kernel matrix $L$. We obtain the first multiplicative approximation guarantee for this problem using local search, a method that has been previously applied to symmetric DPPs. Our approximation factor of $k^{O(k)}$ is nearly tight, and we show theoretically and experimentally that it compares favorably to the state-of-the-art methods for this problem that are based on greedy maximization. The main new insight enabling our improved approximation factor is that we allow local search to update up to two elements of the solution in each iteration, and we show this is necessary to have any multiplicative approximation guarantee.

The first thing I ever bought on Amazon was an edutainment DVD for babies. I don't recall making the purchase, but the data is unequivocal on this point: on 14 November 2004, I bought Baby Einstein: Baby Noah – Animal Expedition for the sum of £7.85. My nearest guess is that I got it as a Christmas present for my nephew, who would at that point have been one year old, and at the very peak of his interest in finger-puppet animals who cavort to xylophone arrangements of Beethoven. This was swiftly followed by three more DVD purchases I have no memory of making. Strangely, I bought nothing at all from Amazon the following year, and then, in 2006, I embarked on a PhD and started ramping up my acquisition of the sort of books that were not easily to be found in brick-and-mortar establishments. Everything ever published by the American novelist Nicholson Baker. I know these things because I recently spent a desultory morning clicking through all 16 years of my Amazon purchase history. Seeing all those hundreds of items bought and delivered, many of them long since forgotten, was a vaguely melancholy experience. I experienced an estranged recognition, as if reading an avant-garde biography of myself, ghost-written by an algorithm. From the bare facts of the things I once bought, I began to reconstruct where I was in life, and what I was doing at the time, and what I was (or wanted to be) interested in. And yet an essential mystery endured.

The idea is to minimize the occurrence of multiple objects from the same cluster in the same set. In the current paper, we study computational aspects of the method. First, we prove that the problem of finding the optimal clustering is NP-hard. Second, to numerically find a suitable clustering, we propose to use the genetic algorithm augmented by a renumbering procedure, a fast task-specific local search heuristic and an initial solution based on a simplified model. Third, in a simulation study, we demonstrate that our improvements of the standard genetic algorithm significantly enhance its computational performance.

Back in 2019, Walmart started piloting its first local fulfillment center in Salem, which uses robots called the Alphabot to pick items from shelves. Now, the retail giant is turning more locations into automated fulfillment centers by converting a portion of the stores into warehouses or adding a new section. Walmart stocks automated fulfillment centers with frequently purchased goods, including consumables (such as fresh and frozen items) and electronics. They're meant to make order delivery and pickup a lot faster, and the Alphabot is a key element in making that possible. The wheeled robot can quickly go anywhere inside a warehouse to retrieve items from shelves and then take them to a workstation for assembly.

This process is called order picking, which may constitute about 50-65% of operating costs. Therefore order picking is considered the highest-priority area for productivity improvements (see De Koster et al. (2007)). In a traditional manual order picking system (also called a picker-to-parts system), the pickers spend 50% of their working time on the task of walking (see Tompkins (2010); for an overview of manual order picking systems see De Koster et al. (2007)). The unproductive working times require the picker-to-parts system to have a large workforce, especially for companies which have millions of small-sized items in large warehouses, such as the retailers Amazon, Alibaba, Zara, Zalando and Walmart. Many of them provide both brick-and-mortar stores and online shops to create a seamless shopping experience for customers (omnichannel flexibility). Due to the diversity of online shops, we concentrate on both single-line and multi-line small-sized orders. Especially during the COVID-19 pandemic, online grocery sales are growing threefold faster (see Fabric (2020)). There are increasing demands for alternative warehousing systems to increase the efficiency of order picking, for example, robot-based compact storage and retrieval systems and robotic mobile fulfillment systems (see more details in Azadeh et al. (2019)). Here we consider a relatively new warehousing concept that does not use expensive fixed hardware and can be easily and quickly implemented, called AGV-assisted picking (see Boysen et al. (2019), Azadeh et al. (2019)).

Today, a war over the value of video game retailer GameStop's stock has caused what market guru Jim Cramer called "the squeeze of a lifetime." Howling with glee along the way, traders on the chaotic and obscene subreddit Wall Street Bets helped push GameStop's stock price up from $20 on January 11 to $73 after traditional analysts deemed the stock a clunker. While this isn't the first time Wall Street Bets has contributed to a surprising market shake-up, GameStop's unlikely trip to the moon is unique in both its velocity and allegations of harassment and hacking that accompanied it. Like other physical retailers, GameStop's business has suffered throughout the last year. Few gamers would rather hit the mall than Amazon's significantly safer "Buy Now" button.

Kroger is testing new smart shopping cart technology in the Cincinnati area that eliminates paying at the checkout. For the past few weeks, Kroger quietly rolled out the new carts at its Madeira store, branded "KrogGo." The technology allows shoppers to load up their cart with groceries, then pay by swiping their credit or debit card at the cart, then head for the parking lot. Using artificial intelligence, the technology will enable shoppers to assemble their order without having to scan items as carts begin to recognize a box of cereal or pound of apples, according to Caper, the New York firm behind the technology. The carts include a built-in scale to measure items sold by weight and a built-in screen that can deliver shopping list recommendations, promotional offers, and wayfinding capabilities.

Today, you'll find a deal on Roomba, a discounted Hydro Flask water bottle and savings on beauty products at Ulta. Get a jumpstart on spring cleaning with discounted iRobot Roomba vacuums. The Roomba i3 is $100 off at $299.99 and the Roomba 675 is $80 off at $199.99, plus iRobot's automatic mopping and sweeping device, the Braava 380t, is discounted to $199.99. Whether you're looking for some new fashionable spring layers or discounted winter gear, United by Blue has got you covered with its end of season sale. Now through the end of January you can save up to 60% sitewide, plus, you can get an extra 50% off sale items with code BYEWINTER.

Slate has relationships with various online retailers. If you buy something through our links, Slate may earn an affiliate commission. We update links when possible, but note that deals can expire and all prices are subject to change. All prices were up to date at the time of publication. Why you want this: As robot vacuums have become increasingly popular, we've had to accept that they are not wholly autonomous.