What is missing Hi guys, it would be really nice if you did some actual work instead of copying my work form my website www.photopea.com, that I have been working on since 2012. Could you maybe imp...
The secret ballot is one of the load-bearing walls of democracy. In Georgia, as in most states, this allows you to know whether your neighbor voted, but never who they voted for. Yet, in multiple states including Georgia, that guarantee is actively at risk.
We give the first polynomial improvements over the textbook algorithms for $3$SUM and All-Pairs Shortest Paths (APSP): we show how to deterministically solve $3$SUM on $n$ integers of polynomial size in $O(n^{1.9992})$ time and APSP on directed $n$-vertex graphs with polynomially bounded integer weights in $O(n^{2.9995})$ time. This refutes the $3$SUM and APSP hypotheses. Using known reductions, we also refute the real-valued versions of the $3$SUM and APSP hypotheses, the Exact Triangle hypothesis, the Zero-Weight $k$-Clique hypotheses, and the three rectangular hinted Online Matrix--Vector conjectures of van den Brand, Nanongkai, and Saranurak, and we give polynomial speedups for a variety of other problems. All of these results follow from a single new algorithm for thin matrix products. Let $X$ be an $N\times D$ integer matrix and $Y$ a $D\times N$ integer matrix with $D\le N^{1/18}$, and let $W$ be any set of at most $N^2/\sqrt D$ positions. We compute the entries $(XY)[I,J]$, $(I,J)\in W$, in $O(N^2/D^{0.063})$ operations, which is polynomially less than the time needed to write down $XY$ or to compute $N^2/\sqrt D$ inner products one by one. We design this algorithm by modifying a variant of Coppersmith's rectangular matrix multiplication algorithm, built from a ten-multiplication identity of Schönhage, to perform only the operations needed for the entries in $W$, and show that few operations are needed. Interpreted as a graph algorithm, this solves the All-Edges Sparse Triangle problem in truly subquadratic time on sparse lopsided tripartite graphs where two parts have $n$ vertices but one part has $n^{\varepsilon}$ vertices for $\varepsilon<0.12$. By known reductions, Exact Triangle, and hence $3$SUM and APSP, reduce to this problem. We also give a data structure version that answers queries for single entries of $XY$, not known in advance.
Unified observability platform for logs, metrics, and traces. AI-native insights, S3-native storage, SQL queries, OpenTelemetry-native, and 80x lower cost than Datadog and Splunk.
Senator Bernie Sanders, Representative Ocasio-Cortez, and Senator Jeff Merkley introduced the Ban Flock Act on Friday, which would stop federal agencies from using automatic license plate readers.
The Global Solar Atlas provides a summary of solar power potential and solar resources globally. It is provided by the World Bank Group as a free service to governments, developers and the general public, and allows users to quickly obtain data and carry out a simple electricity output calculation for any location covered by the solar resource database.
<p>The mathematics of geothermal energy involves the application of various mathematical methods to explore and optimize how geothermal heat from the Earth's interior can be harnessed for energy production and heating. Geothermal energy is derived from the heat generated by the Earth's formation and ongoing radioactive decay, with the temperature increasing significantly with depth, a concept known as the geothermal gradient. High-gradient areas, particularly along tectonic plate boundaries like the Ring of Fire, are prime locations for geothermal energy projects.</p> <p>Mathematicians and engineers utilize models such as Lagrangian–Eulerian flow models to understand fluid movement and its implications for geothermal reservoirs, while stochastic and geometric models help in optimizing energy extraction processes. Additionally, geothermal heat pump systems have been developed to transfer heat for building heating and cooling, though large-scale water movement can lead to geological concerns such as subsidence.</p> <p>Electricity can also be generated from geothermal resources, with power plants utilizing steam to drive turbines. Despite the advantages of geothermal energy, including its low greenhouse gas emissions and reliability compared to other renewable sources, its adoption has been slow due to perceived limitations in quality sites and the high initial capital costs. Nonetheless, renewed interest in geothermal energy is evident, especially amid global concerns about climate change.</p>
Generative AI has been promoted as the technology that could transform education by providing every student a personal tutor. We provide some of the first large-scale experimental evidence, from a two-year cluster randomized trial in 18 Tennessee middle schools in which randomly assigned students used Khan Academy with its AI tutor, Khanmigo, configured to coach rather than give answers, during existing daily remedial mathematics sessions.
A Zen-garden raking puzzle: a novice monk walks into the sand and must rake his way back out to the gate in one stroke. The full design, solver experiments, 148 gardens and a year of daily ones, and a playable prototype, in one page.
Ads – they’re everywhere. The only way to stay sane on the Internet is to attempt to mitigate the horrors of relentless ads. This article summarises how we might still keep the ads under control at the Android platform level in 2026