First thing you should do is make sure Find Hub is enabled. You can do that by downloading and setting up the Find Hub app or going to Settings Google All services Find Hub. After that, set Gemini as your device's assistant by going to the Google app and then tapping on your profile icon at the top right corner of the screen. From there, go to Gemini or Google Assistant Digital assistants from Google. Choose Gemini as the default.

When you purchase through links in our articles, we may earn a small commission. This $12 USB-C hub adds 5 ports your laptop should've had The Ugreen Revodok 5-in-1 USB-C hub adds HDMI, USB-A data, and passthrough charging to any laptop. Wish you had extra USB-A and HDMI slots but don't want to buy a bunch of different adapters to juggle? There's a small accessory you can get that'll solve your woes: the Ugreen 5-in-1 USB-C hub, normally $16 but on sale for $12 right now. This hub turns your laptop's USB-C port into five ports making you give up the USB-C port's charging capabilities.

Don't let busted pipes or an overflowing washing machine dampen your day. Water plays an essential role in our homes, but it can also wreak havoc. Burst pipes, leaky toilets, and misbehaving appliances can stop your day in its tracks. Water leak detectors help reduce the risk by alerting you to problems quickly so you can act to prevent severe damage. Around one in 60 insured homeowners file a claim related to water damage or freezing every year, according to the Insurance Information Institute, and the average cost of the property damage is about $15,000. The longer a leak goes undetected, the more damage it does, destroying furniture and decorations, spawning mold and fungi, and even threatening structural integrity. I've tested many smart leak detectors over the past few years, and these are my favorites. Insurers love them, so before you go shopping, it's worth checking with yours to see what they offer or recommend, and whether installing a leak sensor can reduce your premiums. Shaped like a drop of water, this versatile standalone device alerts you within seconds of detecting a leak and offers compelling extras like temperature tracking at a reasonably affordable price.

When you purchase through links in our articles, we may earn a small commission. Just plug it into your laptop's USB-C port and you're good to go. It's "nothing special" in the sense that these hub ports are exactly what you'd need for day-to-day tasks. We already mentioned the 4K HDMI for hooking up a high-def external monitor, but you also get a 5Gbps USB-C data port, double USB-A ports, and SD/microSD card slots. The final port is USB-C with 100 watts of passthrough charging, which means you can keep your laptop fully charged even while using this hub.

We study the sample complexity of robust binary hypothesis testing under three standard contamination models: $\varepsilon$-additive (Huber), $\varepsilon$-subtractive, and $\varepsilon$-total variation (TV), denoted by $n^*_{\mathrm{Hub}}(\varepsilon)$, $n^*_{\mathrm{Sub}}(\varepsilon)$, and $n^*_{\mathrm{TV}}(\varepsilon)$, respectively. For subtractive contamination, we show that least favourable distributions exist and provide explicit formulas for the same, bringing this model in line with the classical Huber and TV models. Next we show that in all three models, sample complexity may be highly unstable in the contamination parameter $\varepsilon$, increasing by polynomial factors even for $o(\varepsilon)$ perturbations. Similarly, there may be polynomial factor gaps between the sample complexities when $\varepsilon$ is known exactly versus when it is known up to $o(\varepsilon)$ error. Despite the instability of the sample complexity in all models, we show that the sample complexities across models are comparable up to constant-factor rescaling of $\varepsilon$. Specifically, for any fixed $δ_0>0$, the following hold for all distributions $p$ and $q$: (i) $n^*_{\mathrm{Hub}}(\varepsilon) \lesssim n^*_{\mathrm{TV}}(\varepsilon) \lesssim n^*_{\mathrm{Hub}}(2\varepsilon)$, (ii) $n^*_{\mathrm{Sub}}(\varepsilon) \lesssim n^*_{\mathrm{TV}}(\varepsilon) \lesssim n^*_{\mathrm{Sub}}((2+δ_0)\varepsilon)$, and (iii) $n^*_{\mathrm{Sub}}(\varepsilon) \lesssim n^*_{\mathrm{Hub}}(\varepsilon) \lesssim n^*_{\mathrm{Sub}}((1+δ_0)\varepsilon)$, and the scaling constants are tight. Finally, we extend our results to adaptive versions of the contamination models.

Middle-mile logistics describes the problem of routing parcels through a network of hubs, which are linked by a fixed set of trucks. The main challenge comes from the finite capacity of the trucks. The decision to allocate a parcel to a specific truck might block another parcel from using the same truck. It is thus necessary to solve for all parcel routes simultaneously. Exact solution methods scale poorly with the problem size and real-world instances are intractable.

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An example prompt for constructing PDDL models of the action "close a