Related papers: The $\infty$-Oreo$^{^\circledR}$
In this work we extend recent study of the properties of the dense packing of "superdisks," by Y. Jiao, F. H. Stillinger and S. Torquato, Phys. Rev. Lett. 100, 245504 (2008), to the jammed state formed by these objects in random sequential…
A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as $\O$-regions. We argue…
Food texture is a complex property; various sensory attributes such as perceived crispiness and wetness have been identified as ways to quantify it. Objective and automatic recognition of these attributes has applications in multiple…
Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $\omega(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$,…
In the United States the preferred method of obtaining dietary intake data is the 24-hour dietary recall, yet the measure of most interest is usual or long-term average daily intake, which is impossible to measure. Thus, usual dietary…
The fast flavor instability (FFI) is expected to be ubiquitous in core-collapse supernovae and neutron star mergers. It rapidly shuffles neutrino flavor in a way that could impact the explosion mechanism, neutrino signals, mass outflows,…
The Huge Object model is a distribution testing model in which we are given access to independent samples from an unknown distribution over the set of strings $\{0,1\}^n$, but are only allowed to query a few bits from the samples. We…
Let (M, \om) be a symplectic manifold. A Lagrangian fiber bundle \pi : M -> B determines a completely integrable system on M. First integrals of this system are the pull-backs of functions on the base of the bundle. We show that for each…
In this paper, we introduce a flip operation on self-complementary ideals of chain product posets and study the resulting flip graphs. We give asymptotics for the number of vertices in these graphs, compute their diameters, and give bounds…
In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the…
Nowadays millions of images are shared on social media and web platforms. In particular, many of them are food images taken from a smartphone over time, providing information related to the individual's diet. On the other hand, eating…
We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at…
One-year-old infants rapidly form and generalize categories of the everyday objects they encounter. Here we provide evidence on infants daily-life visual experiences for 8 early-learned object categories. Using a corpus of infant…
At the availability of a sharp interconnection, the difference in sizes with Dirac and Pauli form factors of a massive neutrino must constitute their linearly ordered set. Such a class of currents can lead in the field of a spinless nucleus…
We present recursive formulas giving the maximal number of leaves in tree-like polyforms living in two-dimensional regular lattices and in tree-like polycubes in the three-dimensional cubic lattice. We call these tree-like polyforms and…
We study skew-products of the form (x,\omega)\mapsto (Tx, \omega+\phi(x)) where T is a nonuniformly expanding map on a space X, preserving a (possibly singular) probability measure \tilde\mu, and \phi:X\to S^1 is a C^1 function. Under mild…
In this paper we prove a family of results connecting the problem of computing cup products in surface bundles to various other objects that appear in the theory of the cohomology of the mapping class group $\operatorname{Mod}_g$ and the…
We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly…
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling…
We investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents who may have different entitlements. We characterize the existence of a connected strongly-proportional allocation…