1,078 research outputs found
Constructive Tensor Field Theory: The Model
We build constructively the simplest tensor field theory which requires some
renormalization, namely the rank three tensor theory with quartic interactions
and propagator inverse of the Laplacian on . This superrenormalizable
tensor field theory has a power counting almost similar to ordinary .
Our construction uses the multiscale loop vertex expansion (MLVE) recently
introduced in the context of an analogous vector model. However to prove
analyticity and Borel summability of this model requires new estimates on the
intermediate field integration, which is now of matrix rather than of scalar
type.Comment: 24 pages, 5 figures. Substantially improved version. Version v1 is
correct but treats a model which is simplified at the level of the two point
function. This version treats the full model, without any simplificatio
Graph properties of graph associahedra
A graph associahedron is a simple polytope whose face lattice encodes the
nested structure of the connected subgraphs of a given graph. In this paper, we
study certain graph properties of the 1-skeleta of graph associahedra, such as
their diameter and their Hamiltonicity. Our results extend known results for
the classical associahedra (path associahedra) and permutahedra (complete graph
associahedra). We also discuss partial extensions to the family of nestohedra.Comment: 26 pages, 20 figures. Version 2: final version with minor correction
Compatibility fans for graphical nested complexes
Graph associahedra are natural generalizations of the classical associahedra.
They provide polytopal realizations of the nested complex of a graph ,
defined as the simplicial complex whose vertices are the tubes (i.e. connected
induced subgraphs) of and whose faces are the tubings (i.e. collections of
pairwise nested or non-adjacent tubes) of . The constructions of M. Carr and
S. Devadoss, of A. Postnikov, and of A. Zelevinsky for graph associahedra are
all based on the nested fan which coarsens the normal fan of the permutahedron.
In view of the combinatorial and geometric variety of simplicial fan
realizations of the classical associahedra, it is tempting to search for
alternative fans realizing graphical nested complexes.
Motivated by the analogy between finite type cluster complexes and graphical
nested complexes, we transpose in this paper S. Fomin and A. Zelevinsky's
construction of compatibility fans from the former to the latter setting. For
this, we define a compatibility degree between two tubes of a graph . Our
main result asserts that the compatibility vectors of all tubes of with
respect to an arbitrary maximal tubing on support a complete simplicial fan
realizing the nested complex of . In particular, when the graph is
reduced to a path, our compatibility degree lies in and we recover
F. Santos' Catalan many simplicial fan realizations of the associahedron.Comment: 51 pages, 30 figures; Version 3: corrected proof of Theorem 2
Geometric realizations of the accordion complex of a dissection
Consider points on the unit circle and a reference dissection
of the convex hull of the odd points. The accordion complex
of is the simplicial complex of non-crossing subsets of the
diagonals with even endpoints that cross a connected subset of diagonals of
. In particular, this complex is an associahedron when
is a triangulation and a Stokes complex when
is a quadrangulation. In this paper, we provide geometric
realizations (by polytopes and fans) of the accordion complex of any reference
dissection , generalizing known constructions arising from
cluster algebras.Comment: 25 pages, 10 figures; Version 3: minor correction
Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
Ordinary tensor models of rank are dominated at large by
tree-like graphs, known as melonic triangulations. We here show that
non-melonic contributions can be enhanced consistently, leading to different
types of large limits. We first study the most generic quartic model at
, with maximally enhanced non-melonic interactions. The existence of the
expansion is proved and we further characterize the dominant
triangulations. This combinatorial analysis is then used to define a
non-quartic, non-melonic class of models for which the large free energy
and the relevant expectations can be calculated explicitly. They are matched
with random matrix models which contain multi-trace invariants in their
potentials: they possess a branched polymer phase and a 2D quantum gravity
phase, and a transition between them whose entropy exponent is positive.
Finally, a non-perturbative analysis of the generic quartic model is performed,
which proves analyticity in the coupling constants in cardioid domains
Learning to Avoid Luck Traps in Contexts of Uncertainty A Review of Jeffrey Rosenthal’s Knock on Wood: Luck, Chance, and the Meaning of Everything
In the field of probability instruction, much has been written about the increasingly important role of uncertainty and probability in our everyday lives. This work similarly highlights the key role that probability plays in a growing number of professional areas
Successful rescue therapy with tenofovir in a patient with hepatic decompensation and adefovir resistant HBV mutant
BACKGROUND: Prolonged adefovir therapy exposes to the emergence of adefovir resistant hepatitis B virus mutants. Initial reports of the rtN236T mutation showed preserved sensitivity to lamivudine; however, complex mutations are emerging with reduced susceptibility to lamivudine. CASE PRESENTATION: After 2 years of therapy, a cirrhotic patient developed the rtN236T and rtA181T adefovir resistant mutations. He had been previously treated with lamivudine, developed lamivudine resistance and, despite good compliance, had an incomplete response to adefovir. Adefovir resistance resulted in viral breakthrough with hepatitis flare-up and liver decompensation. Tenofovir had an excellent antiviral effect allowing sustained control of viral replication and reversal of hepatic failure. CONCLUSION: In patients with cirrhosis, adefovir resistance can lead to severe hepatitis. Tenofovir appears to be an effective treatment of adefovir resistant mutants. Incomplete control of viral replication with adefovir requires monitoring for viral resistance and should prompt a change in antiviral treatment
On the Fairness ROAD: Robust Optimization for Adversarial Debiasing
In the field of algorithmic fairness, significant attention has been put on
group fairness criteria, such as Demographic Parity and Equalized Odds.
Nevertheless, these objectives, measured as global averages, have raised
concerns about persistent local disparities between sensitive groups. In this
work, we address the problem of local fairness, which ensures that the
predictor is unbiased not only in terms of expectations over the whole
population, but also within any subregion of the feature space, unknown at
training time. To enforce this objective, we introduce ROAD, a novel approach
that leverages the Distributionally Robust Optimization (DRO) framework within
a fair adversarial learning objective, where an adversary tries to infer the
sensitive attribute from the predictions. Using an instance-level re-weighting
strategy, ROAD is designed to prioritize inputs that are likely to be locally
unfair, i.e. where the adversary faces the least difficulty in reconstructing
the sensitive attribute. Numerical experiments demonstrate the effectiveness of
our method: it achieves Pareto dominance with respect to local fairness and
accuracy for a given global fairness level across three standard datasets, and
also enhances fairness generalization under distribution shift.Comment: 23 pages, 10 figure
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