58,703 research outputs found

### Efficient inference in the transverse field Ising model

In this paper we introduce an approximate method to solve the quantum cavity
equations for transverse field Ising models. The method relies on a projective
approximation of the exact cavity distributions of imaginary time trajectories
(paths). A key feature, novel in the context of similar algorithms, is the
explicit separation of the classical and quantum parts of the distributions.
Numerical simulations show accurate results in comparison with the sampled
solution of the cavity equations, the exact diagonalization of the Hamiltonian
(when possible) and other approximate inference methods in the literature. The
computational complexity of this new algorithm scales linearly with the
connectivity of the underlying lattice, enabling the study of highly connected
networks, as the ones often encountered in quantum machine learning problems

### The Topology of Negatively Associated Distributions

We consider the sets of negatively associated (NA) and negatively correlated
(NC) distributions as subsets of the space $\mathcal{M}$ of all probability
distributions on $\mathbb{R}^n$, in terms of their relative topological
structures within the topological space of all measures on a given measurable
space. We prove that the class of NA distributions has a non-empty interior
with respect to the topology of the total variation metric on $\mathcal{M}$. We
show however that this is not the case in the weak topology (i.e. the topology
of convergence in distribution), unless the underlying probability space is
finite. We consider both the convexity and the connectedness of these classes
of probability measures, and also consider the two classes on their (widely
studied) restrictions to the Boolean cube in $\mathbb{R}^n$

### Nonlinear realisation approach to topologically massive supergravity

We develop a nonlinear realisation approach to topologically massive
supergravity in three dimensions, with and without a cosmological term. It is a
natural generalisation of a similar construction for ${\cal N}=1$ supergravity
in four dimensions, which was recently proposed by one of us. At the heart of
both formulations is the nonlinear realisation approach to gravity which was
given by Volkov and Soroka fifty years ago in the context of spontaneously
broken local supersymmetry. In our setting, the action for cosmological
topologically massive supergravity is invariant under two different local
supersymmetries. One of them acts on the Goldstino, while the other
supersymmetry leaves the Goldstino invariant. The former can be used to gauge
away the Goldstino, and then the resulting action coincides with that given in
the literature.Comment: 29 page

### Rank-based linkage I: triplet comparisons and oriented simplicial complexes

Rank-based linkage is a new tool for summarizing a collection $S$ of objects
according to their relationships. These objects are not mapped to vectors, and
``similarity'' between objects need be neither numerical nor symmetrical. All
an object needs to do is rank nearby objects by similarity to itself, using a
Comparator which is transitive, but need not be consistent with any metric on
the whole set. Call this a ranking system on $S$. Rank-based linkage is applied
to the $K$-nearest neighbor digraph derived from a ranking system. Computations
occur on a 2-dimensional abstract oriented simplicial complex whose faces are
among the points, edges, and triangles of the line graph of the undirected
$K$-nearest neighbor graph on $S$. In $|S| K^2$ steps it builds an
edge-weighted linkage graph $(S, \mathcal{L}, \sigma)$ where $\sigma(\{x, y\})$
is called the in-sway between objects $x$ and $y$. Take $\mathcal{L}_t$ to be
the links whose in-sway is at least $t$, and partition $S$ into components of
the graph $(S, \mathcal{L}_t)$, for varying $t$. Rank-based linkage is a
functor from a category of out-ordered digraphs to a category of partitioned
sets, with the practical consequence that augmenting the set of objects in a
rank-respectful way gives a fresh clustering which does not ``rip apart`` the
previous one. The same holds for single linkage clustering in the metric space
context, but not for typical optimization-based methods. Open combinatorial
problems are presented in the last section.Comment: 37 pages, 12 figure

### Graph Convex Hull Bounds as generalized Jensen Inequalities

Jensen's inequality is ubiquitous in measure and probability theory,
statistics, machine learning, information theory and many other areas of
mathematics and data science. It states that, for any convex function $f\colon
K \to \mathbb{R}$ on a convex domain $K \subseteq \mathbb{R}^{d}$ and any
random variable $X$ taking values in $K$, $\mathbb{E}[f(X)] \geq
f(\mathbb{E}[X])$. In this paper, sharp upper and lower bounds on
$\mathbb{E}[f(X)]$, termed "graph convex hull bounds", are derived for
arbitrary functions $f$ on arbitrary domains $K$, thereby strongly generalizing
Jensen's inequality. Establishing these bounds requires the investigation of
the convex hull of the graph of $f$, which can be difficult for complicated
$f$. On the other hand, once these inequalities are established, they hold,
just like Jensen's inequality, for any random variable $X$. Hence, these bounds
are of particular interest in cases where $f$ is fairly simple and $X$ is
complicated or unknown. Both finite- and infinite-dimensional domains and
codomains of $f$ are covered, as well as analogous bounds for conditional
expectations and Markov operators.Comment: 12 pages, 1 figur

### Entanglement entropy for spherically symmetric regular black holes

The Bardeen and Hayward spacetimes are here considered as standard
configurations of spherically symmetric regular black holes. Assuming the
thermodynamics of such objects to be analogous to standard black holes, we
compute the island formula in the regime of small topological charge and vacuum
energy, respectively for Bardeen and Hayward spacetimes. Late and early-time
domains are separately discussed, with particular emphasis on the island
formations. We single out conditions under which it is not possible to find out
islands at early-times and how our findings depart from the standard
Schwarzschild case. Motivated by th fact that those configurations extend
Reissner-Nordstr\"{o}m and Schwarzschild-de Sitter metrics through the
inclusion of regularity behavior at $r=0$, we show how the effects of
regularity induces modifications on the overall entanglement entropy. Finally,
the Page time is also computed and we thus show which asymptotic values are
expected for it, for all the configurations under exam. The Page time shows
slight departures than the Schwarzschild case, especially for the Hayward case,
while the Bardeen regular black hole turns out to be quite indistinguishable
from the Schwarzschild case.Comment: 11 pages, 4 table

### Can you hear your location on a manifold?

We introduce a variation on Kac's question, "Can one hear the shape of a
drum?" Instead of trying to identify a compact manifold and its metric via its
Laplace--Beltrami spectrum, we ask if it is possible to uniquely identify a
point $x$ on the manifold, up to symmetry, from its pointwise counting function
$N_x(\lambda) = \sum_{\lambda_j \leq \lambda} |e_j(x)|^2,$ where here $\Delta_g e_j = -\lambda_j^2 e_j$ and $e_j$ form an orthonormal
basis for $L^2(M)$. This problem has a physical interpretation. You are placed
at an arbitrary location in a familiar room with your eyes closed. Can you
identify your location in the room by clapping your hands once and listening to
the resulting echos and reverberations?
The main result of this paper provides an affirmative answer to this question
for a generic class of metrics. We also probe the problem with a variety of
simple examples, highlighting along the way helpful geometric invariants that
can be pulled out of the pointwise counting function $N_x$.Comment: 26 pages, 1 figur

### Barren plateaus in quantum tensor network optimization

We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer

### Less sculptural more intellectual: conceptualizing landscape in the architecture of 1990s and 2000s

The aim of this paper is to discuss the radical shift which emerges in the 1990s and enhances architecture in the 2000s by turning it into a less sculptural more intellectual field of design. Hence, architects rather focus on ground than figure in design projects. This leads them to interrogate the conventional relationships between figure and ground enabling figure to dominate the ground in architecture for decades. They discover the mutual relationships between figure and ground, and design grounded structures instead of ungrounded sculptures. These artificial structures seem like the extensions of the natural landscape, as such the conceptual and categorical distinction between artificial and natural blurs in architecture. Another conceptual blurring emerges between the concepts of landscape, ground, and field. These are generally used as interchangeable concepts, but landscape encompasses ground and field, making it a more comprehensive concept for architects. It is revealed in the paper that landscape is a re-emerging concept which refers to the conceptual shift from form and function to flow and force in architecture. Landscape, therefore, awaits to be explored as a field of flows and forces by even more architects in this century in which cities are characterized by sculptural forms and objects

### Changes in PRC1 activity during interphase modulate lineage transition in pluripotent cells

The potential of pluripotent cells to respond to developmental cues and trigger cell differentiation is enhanced during the G1 phase of the cell cycle, but the molecular mechanisms involved are poorly understood. Variations in polycomb activity during interphase progression have been hypothesized to regulate the cell-cycle-phase-dependent transcriptional activation of differentiation genes during lineage transition in pluripotent cells. Here, we show that recruitment of Polycomb Repressive Complex 1 (PRC1) and associated molecular functions, ubiquitination of H2AK119 and three-dimensional chromatin interactions, are enhanced during S and G2 phases compared to the G1 phase. In agreement with the accumulation of PRC1 at target promoters upon G1 phase exit, cells in S and G2 phases show firmer transcriptional repression of developmental regulator genes that is drastically perturbed upon genetic ablation of the PRC1 catalytic subunit RING1B. Importantly, depletion of RING1B during retinoic acid stimulation interferes with the preference of mouse embryonic stem cells (mESCs) to induce the transcriptional activation of differentiation genes in G1 phase. We propose that incremental enrolment of polycomb repressive activity during interphase progression reduces the tendency of cells to respond to developmental cues during S and G2 phases, facilitating activation of cell differentiation in the G1 phase of the pluripotent cell cycle

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