We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such that the variance of $f$ is $Ω(1)$ and all its individual influences are bounded by $τ$. We show...
Let’s face it: the hardware hike of PC gaming has been getting out of control. AAA developers are constantly pushing increasingly demanding graphics with diminishing returns, and PC gamers have been...
Consider a function that is mildly hard for size-$s$ circuits. For sufficiently large $s$, Impagliazzo's hardcore lemma guarantees a constant-density subset of inputs on which the same function is extremely hard for circuits of size $s'<\!\!<s$. Blan...
random thought: smart houses, appliances, televisions, phones, devices, etc. are constantly watching us...we live in a surveillance state...big brother is watching ?...
We are interested in time-harmonic acoustic scattering by an impenetrable obstacle in a medium where the wavenumber is constant in an exterior unbounded subdomain and is possibly heterogeneous in a bounded subdomain. The associated Helmholtz boundary...
We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are known for cy...
One of the distinct features of this century has been the population of older adults which has been on a constant rise. Elderly people have several needs and requirements due to physical disabilities, cognitive issues, weakened memory and disorganize...
Not one day passes without an incident. Not one. Since July there have been constant attacks. The city does not have enough resources to tackle what’s going on. What will happen is the unaffected ...
A geometric formulation of a generalization of Nambu mechanics is proposed. This formulation is carried out, wherever possible, in analogy with that of Hamiltonian systems. In this formulation, a strictly nondegenerate constant 3-form is attached t...
In this work, we present a general framework for the design and analysis of two-level AMG methods. The approach is to find a basis for locally optimal or quasi-optimal coarse space, such as the space of constant vectors for standard discretizations o...
Funding is a cost to trading desks that they see as an input. Current FVA-related literature reflects this by also taking funding costs as an input, usually constant, and always risk-neutral. However, this funding curve is the output from a Treasury...
In this article, we study a particular group of plane figures whose constants are listed in the Susa Mathematical Tablet No.\,3 (\textbf{SMT No.\,3}). We explain possible ways to define these figures and seek to demonstrate that the Susa scribes used...
We consider the random regular $k$-NAE-SAT problem with $n$ variables each appearing in exactly $d$ clauses. For all $k$ exceeding an absolute constant $k_0$, we establish explicitly the satisfiability threshold $d_*=d_*(k)$. We prove that for $d<d_*...
We determine the asymptotics of the independence number of the random $d$-regular graph for all $d \ge d_0$. It is highly concentrated, with constant-order fluctuations around $nα_* - c_*\log n$ for explicit constants $α_*(d)$ and $c_*(d)$. Our pro...
until the Emperor Constantine made the seven-day week official in AD 321; thereafter, the seven-day week spread throughout the Roman Empire and eventually
Sudbury (1985) showed for the Maki-Thompson model of rumour spreading that the proportion of the population never hearing the rumour converges in probability to a limiting constant (approximately equal to 0.203) as the population size tends to infini...
What, if any, was Einstein's biggest mistake, the one most affecting our physics today? There is a perhaps apocryphal story, recounted by George Gamow, that he counted his cosmological constant as his biggest blunder. We now know his hypothesized cos...
If you prioritize something, you treat it as more important than other things. Prioritize your own wants rather than constantly thinking about others.
Background: Open Source Software (OSS) started as an effort of communities of volunteers, but its practices have been adopted far beyond these initial scenarios. For instance, the strategic use of OSS in industry is constantly growing nowadays in dif...
28M Followers, 887 Following, 4,256 Posts - Nina Dobrev (@nina) on Instagram: "I live on the edge… and constantly fall off it ?"